If one said Vesein Tal Umatar prior/post its allowed time:
If one said Vesein Tal Umatar Levracha during the summer, outside of its allowed time, which is between Pesach and 7th Cheshvan or 5th December, there is a difference in law between Eretz Yisrael and the Diaspora.
Eretz Yisrael: In Eretz Yisrael, if one said Vesein Tal Umatar after Pesach, [during the summer, which is any time between Chol Hamoed Pesach and the 7th of Marcheshven], one is required to go back and repeat from the beginning of Barecih Aleinu. If one already conclude Shemoneh Esrei then he must repeat it.
Diaspora-between Pesach and Shemini Atzeres: In the Diaspora, if one said Vesein Tal Umatar after Pesach, [during the summer, which is any time between Chol Hamoed Pesach and Shemini Atzeres], then if one is in a country that as a whole does not need rain during the summer, it follows the same ruling as Eretz Yisrael, and one must go back to Bareich Aleinu or repeat Shemoneh Esrei. If however one’s country as a whole requires rain even during the summer months, then one who said Vesein Tal Umatar during those months is not required to go back and repeat from the beginning of Bareich Aleinu. Nevertheless, if one wills he may repeat the Shemoneh Esrei as a Tefilas Nedava.
Diaspora-between Shemini Atzeres and the 7th of Cheshvan: If one asked for rain after Sukkos, prior to the 7th of MarCheshvan, according to Admur and other Poskim, Shemoneh Esrei is to be repeated. See Q&A!
Diaspora-between 7th of Cheshvan and 5th of December: In those countries [that in general need rain after Sukkos and that’s when their rain season begins], if one said Vesein Tal Umatar after the 7th of Cheshven, prior to the 5th of December, he is not required to go back, or repeat Shemoneh Esrei. [This applies even if his country is not currently in need of rain, such as it already rained plently, so long as it is a general time that the country needs rain. If, however, the country is not yet in need of rain, then Shemoneh Esrei is to be repeated if rain was mentioned prior to the 5th of December.] Nevertheless if one wills he may repeat the Shemoneh Esrei as a Tefilas Nedava.
If one mistakenly said Visein Tal Umatar between Shemini Atzeres and the 7th of Marcheshvan, is he to repeat Shemoneh Esrei?
 Admur 117/1 and 3; Michaber 117/2-3
 Admur 117/3; Michaber 117/3
 Michaber ibid
 See Q&A that according to Admur and other Poskim this applies even after Sukkos, before the 7th of Cheshvan, although other Poskim argue.
 Admur 117/1; Michaber 117/2; Rama 117/2; Rosh
 Michaber ibid
 Background of this ruling:
 Admur 117/1; Mateh Moshe 1/141; Elya Raba 117/3; Radbaz 6/2; Olas Tamid 117/3; Kneses Hagedola 117/4; Soles Belula 117/1; Birkeiy Yosef 117/3; Beir Heiytiv 117/6; Tehila Ledavid 117/1-2; Biur Halacha 117/1 “Hatzerichim”; Kaf Hachaim 117/8; Ketzos Hashulchan 21/8; Poskim in Piskeiy Teshuvos 117/4 footnote 33
Other opinions: Some Poskim rule that all countries in the Diaspora are to repeat Shemoneh Esrei prior to the 5th of December. [Maharikash, brought in Birkeiy Yosef ibid and Kaf Hachaim ibid, in argument against the Radbaz]
 Admur 117/1 “these lands whose planting season is in Tishreiy need rain after Sukkos otherwise the seeds that were planted will be destroyed”; Peri Chadash 117, brought in Beir Heiytiv 117/6; Mamar Mordechai 117/8; Biur Halacha 117 “Hatzerichim”; Tehila Ledavid 117/1-2; Kaf Hachaim 117/8 that so is implication of all Poskim ibid, unlike Beir Heiytiv
 Ketzos Hashulchan 21/8
 Ketzos Hashulchan 21/8 footnote 21 in implication of Admur ibid who does not make any such differentiation; Implication of Rosh, brought in M”A 117/4 and Machatzis Hashekel ibid; Biur Halacha 117/1 “Hatzerichin”; Piskeiy Teshuvos 117/4
Other opinions: Some Poskim question that perhaps the above law that one does not have to repeat only applies if there is currently a droubt in the country and it is in need of rain, otherwise, he must repeat Shemoneh Esrei, even though it is currently the rain season in his country. [M”A 117/4 in implication of Michaber 117/2]
 Implication of Admur ibid who writes the ruling of not repeating Shemoneh Esrei to only “these countries” and these countries refer to “these lands whose planting season is in Tishreiy need rain after Sukkos otherwise the seeds that were planted will be destroyed”, hence implying that countries that do not need rain after Sukkos, one must repeat Shemone Esrei prior to the 5th of December; See also Ketzos Hashulchan 21/8 “a country whose rain season is at that time”; Peri Chadash 117, brought in Beir Heiytiv 117/6; Mamar Mordechai 117/8; Biur Halacha 117 “Hatzerichim”; Tehila Ledavid 117/1-2; Kaf Hachaim 117/8 that so is implication of all Poskim ibid, unlike Beir Heiytiv;
Other opinions: Some Poskim rule that all countries are exempt from repeating Shemoneh Esrei between the 7th of Cheshvan and the 5th of December. [Beir Heiytiv 117/6 that so is implication of Mateh Moshe 1/141, Radbaz 6/2-58, Olas Tamid 117/3, Kneses Hagedola 117 [However see Mamar Mordechai 117/8 and Kaf Hachaim 117/8 who argues on Beir Heiytiv]; Toras Chaim 3/3 [Maharchash-Rav Chaim Shabsi of Salunki, Greece 1600] brought in Rav Akiva Eiger 117; Toras Chaim Sofer 117/6; Piskeiy Teshuvos 117/4]
 The reason:
 Toras Chaim 3/3 [Maharchash-Rav Chaim Shabsi of Salunki, Greece 1600] brought in Rav Akiva Eiger 117; Tehila Ledavid 117/1-2; Toras Chaim Sofer 117/6; Orchos Chaim Spinka 117/1; Rav SZ”A in Halichos Shlomo 8/18; Or Letziyon 2/7-31; Yabia Omer 5/15; 10/10; The following Rishonim rule that one may even initially ask for rain in Eretz Yisrael from after Sukkos: Ritva.
 The reason: As after Sukkos it is no longer a Siman Kelala to have rain, and thus we begin saying Mashiv Haruach, and only when it’s a Siman Kelala do we make one repeat Shemoneh Esrei. [Toras Chaim ibid; Tehila Ledavid ibid; Toras Chaim Sofer ibid]
 Poskim ibid
Does this apply in all countries that don’t need rain before the 7th of Marcheshvan? Some of the Poskim ibid imply that their ruling applies in all countries, as there is no country in which rain is a Siman Kelala after Sukkos. This is also implied from the fact they plainly state that in all the Diaspora there is no need to repeat Shemoneh Esrei without making any differentiation. [See Toras Chaim and Toras Chaim Sofer ibid] However the Tehila Ledavid ibid implies that this ruling only applies to lands that need rain after Sukkos, and not to all lands.
 See Michaber 117/1 and 117/3; Admur 117/1; Mateh Moshe 1/141; Elya Raba 117/3; Radbaz 6/2; Olas Tamid 117/3; Kneses Hagedola 117; Beir Heiytiv 117/6; Biur Halacha 117/1 “Hatzerichim”; Ketzos Hashulchan 21/8
Background: So is implied from Setimas Haposkim who do not state that after Sukkos, before 7th of Cheshvan, has a different status: See Michaber 117/1 “In the rain season one must say Visein Tal Umatar and in…Eretz Yisrael one begins from the 7th of Cheshvan.” Then in Michaber 117/3 “If one asked for rain in the summer months he must repeat”; So also rules without making a differentiation all other Poskim who record this Halacha. In addition, it is clearly evident from the following Poskim that prior to the 7th of Cheshvan one must repeat Shemoneh Esrei, as they rule that in the Diaspora Bedieved one need not repeat Shemoneh Esrei if he said Visein Tal Umatar prior to the 5th of December. However, they stipulate that this only applies after the 7th of Cheshvan, hence implying that if it was said before the 7th of Cheshvan then it needs to be repeated: So rules: Admur 117/1; Mateh Moshe 1/141; Olas Tamid 117/3; Kneses Hagedola 117; Elya Raba 117/3; Beir Heiytiv 117/6; Biur Halacha 117/1 “Hatzerichim”; Ketzos Hashulchan 21/8
 Chazon Ish in Dinim Vehanhagos 4/26; Lehoros Nasan 7/5; Avnei Yishpa 1/16; Koveitz Mibeis Levi 17/99 in name of Rav Wozner
 The reason: Possibly the reason is as follows: a) Once the Sages made their Takana not to say Visein Tal Umatar before the 7th of Cheshvan, Shemoneh Esrei must be repeated if one made a mistake, as although it is not a Siman Kelala, since in majority of the summer it is a Siman Kelala, therefore they did not differentiate in their decree. [See Admur 114/5 for a similar ruling regarding one who said Mashiv Haruach during after Pesach when it is still the rain season] b) Perhaps it is a Siman Kelala to have rain fall on the pilgrims returning from Jerusalem! Now, although we said before that if an entire country needs rain in the summer, then Bedieved if one requested in the summer he does not need to repeat, and the same should seemingly apply here, that if the country needs rain after Sukkos they should not need to repeat, seemingly that was only said regarding countries with a summer rain season, while those with a winter rainseason, must wait unti the 7th of Cheshvan.
 See Admur 117/1; Unedited Sicha of 7th of Cheshvan 1986 [printed in Hisvadyus 1986 1 p. 509] “It is forbidden to ask for rain prior to the 7th of Cheshvan and if one does so he does not fulfill his obligation and must repeat the prayer”; However, in the tape of this Sicha the Rebbe stated that there is a question in what to do if one did so, and did not give a final ruling on the subject.
Background: See Admur 117/1 “The same applies if in these lands an individual made a mistake and asked for rain from the 7th of Cheshvan and onwards he is not required to repeat” Thus, clearly implying that before the 7th he must repeat, unlike the ruling of the former Poskim who say no one has to repeat starting from after Sukkos. This is furthermore implied from the fact Admur ibid limits the ruling of the Mateh Moshe to only “these lands”, hence proving that not being a Siman Kelala is not enough and there has to actually be in need for rain. This defies the entire reason of logic of the lenient Poskim.