My opponent has Hwei on base and plays a Tide Turner on base. Declines to move anything. Does a trigger still occur that creates a chain I can react to?

No. Tideturner's "you may" is decided during finalization — if its controller declines, the ability is removed from the chain and never becomes a Finalized Chain Item, so no chain exists and you get no reaction window.

This follows Rule 383.3.a.2 (a "you may" that leads the effect decides whether the ability is performed at all; declining means it "is removed from the chain and considered to have not triggered"). It also doesn't matter that Hwei is at Base: "another location" excludes Base, so there was no legal swap target anyway (Rule 402.4). Note that even when the trigger is performed, you couldn't react to Tideturner entering play itself — you can only react to the play-effect chain that follows (FAQ #6244).