The Mishnah Berurah (Oraḥ Ḥayim 25:4, s.q. 14) clarifies that the reason one must be careful while reciting Shema' Yisra'el (and the 'Amidah) to also don tephillin is so as not to appear as a false witness (since Shema' Yisra'el mentions wearing tephillin and one who recites it without tephillin appears to be saying one thing and doing another).
The Mishnah Berurah (Oraḥ Ḥayim 34:2, s.q. 15) cites this same reasoning to explain why one must also recite (the first two paragraphs) of Shema' Yisra'el while donning Rabbe'inu Tam tephillin.
I'm having difficulty understanding the Mishnah Berurah's logic in Siman 34. The concern about donning (any) tephillin while reciting Shema' Yisra'el is that in doing so one appears to be a false witness. But, that's only true when one is required to recite Shema'. In the case of Rabbe'inu Tam tephillin being donned after one already recited Shema' Yisra'el (and the 'Amidah) while donning RaSh"I tephillin, why one must one recite anything?
In summary, my understanding of the Mishnah Berurah in Siman 25 is "if Shema' then tephillin" whereas in Siman 34 it appears that the logic is reversed (i.e. "if tephillin then Shema'"). Can someone please help me explain what appears IMHO to be reverse logic?