Q. Is it permitted for one who davens Minhag Aschkenaz to refrain from answering Amein to “V’yatzmach Purkanei Vikareiv M’shichei” since according to his Poskim this addition is a “Shinui Mimadbei’a SheTav’u Chachomim”?

A. Igrois Moshe (O.H. 2: 23) rules that recitations that are said only when there is a tzibur of ten present such as kadish and kedusha should be recited together with them in the nusach of the tzibur, even by those who usually keep a different nusach and he recites them quietly. Similar responses are given by Minchas Yitzvhok (7: 5), Avnei Yoshfe (14) and others.
Therefore Horav Shlomo Miller’s Shlit’a opinion is that one who maintains nusach Ashkenaz should answer V’yatzmach Purkanei Vikareiv M’shichei together with the rest of the tzibur.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a