So, I think the answer to this is ambiguous, in true Guardian fashion. There are interpretations where Shen Wei has no idea it's time travel - doesn't even figure it out when he meets Zhao Yunlan again. And then there's the "he probably figured it out" school of thought.

I think canonically there is no indication of what Shen Wei actually thinks, but Kunlun does tell bb!Shen Wei he hasn't changed in ten thousand years. So that hint really is right there for him to pick up!