If you have a Hwei at a battlefield and the play Tide Turner to swap their locations, does it count as a move for Hwei so his ability activates?

Yes, it counts as a move and triggers Hwei's ability — as long as Tideturner is at a different location from Hwei when you play it.

Tideturner enters play at its own location, then its "When you play me" ability swaps the two units. Since Hwei actually changes battlefield locations (Battlefield A → Battlefield B), that's a zone-change Move per Rule 441, which is exactly what "When I move" checks for.

The nuance comes from FAQ #11643: if Tideturner and Hwei were somehow on the same battlefield, the swap would just exchange their positions within the same location — no meaningful move, no trigger. So as long as they start on different battlefields, Hwei's ability fires: draw 1, discard 1, then the bonus depending on the discarded card's type.