Does bouncing Tideturner cancel its trigger?

No — the trigger isn't cancelled or countered. It still finalizes and resolves, it just resolves with no effect, so the swap never happens.

Tideturner's ability needs its own "original location," and that referent is checked when the instruction executes (Rule 359.3.f.2.a). Once it's been Gusted back to hand, Tideturner is in a non-board zone and returns null for its original location, so the instruction to move the chosen unit there is ignored. Same result if Tideturner is killed or otherwise removed before the trigger resolves — nothing moves, and the unit you targeted stays where it is (FAQ #1694).