Both the Baal Tokeia and the listeners must stand while the Shofar is being blown during the Chazan’s repetition of Musaf. [However Bedieved one fulfills his obligation even if he remained seated.] However by the Tekios of Meyushav the congregation is not required to stand.
 Admur 592/2; Levush 585/1; M”A 592/1; M”B 592/2; Kaf Hachaim 592/3
 The reason for this is because the congregants are required to stand during Chazaras Hashatz. [Admur 124/7 in parentheses going according to the opinion that requires standing by Chazaras Hashatz. However see Piskeiy Teshuvos 124/10 that today many are lenient to sit by Chazaras Hashatz.]
Other reasons: Some Poskim rule that the reason one is required to stand for the Tekios Meumad is because even the listeners are included in the juxtaposition of the above verse and since the Tekios Meumad is the fulfillment of the main Mitzvah of Shofar, therefore also the listeners must stand. [Radbaz 1/25; Mor Uketzia 585; Elya Raba 585/2; Mateh Yehuda; Machazik Bracha 585/1; Erech Hashulchan 585/1; Kaf Hachaim 585/2]
 P”M 592 A”A 1; M”B ibid; Kaf Hachaim ibid
 As explained in 585/2; See Chapter 2 Halacha 5