Rashi’s commentary, Rabbeinu Tam tefillin, and the mesorah of Yemenite Jews

There was a discussion in my Yemenite Beit Knesset a couple weeks ago about Rabbeinu tam’s tefillin, and they were saying that Rabbeinu Tam’s tefillin did not exist in Yemen. Rashi’s commentaries are a part of the Yemenite Mesorah, but 2 generations later (Rabbeinu Tam), is not. My question is did the Yemenites simply not accept Rabbeinu Tam tefillin, or did they never even HEAR about it? Some Sephardim put on Rabbeinu tam tefillin (granted for kabalistic reasons), but it’s clear that Rabbeinu Tam tefillin was known about and some either accepted or rejected, hence my question about Yemenites, since they were relatively more isolated than other Jewish communities.