Based on Ahnald's testing stream: When Windu uses This Party's Over. If the ally doesn't actually assist because Windu attacks first, then there seems to be no swap of turn meter.. Deal Special ...
If the assist is actually a requirement of the TM swap - well, that's actually super stupid but on the other hand it is also super consistent with other effects interfering with the assist.
I think the whole assist thing is handler pretty poorly and is full of self-contradicting things but this would just fit perfectly into that line of weirdos.