Opponent uses Bellows Breath and targets a unit at base. I react with a Tideturner at a bf and swap the targeted unit and the Tideturner. Does the targeted unit take damage?

Ruling

Yes, the targeted unit takes damage.

According to FAQ 7422, the "same location" requirement for Bellows Breath is a targeting restriction, not a resolution requirement. If a target moves after the spell is placed on the chain, the spell still resolves and tracks the target to its new location to deal damage.

Sequence of Events

1. Opponent plays Bellows Breath: They target a unit at your base. The target is locked when the spell is placed on the chain.
2. You react with Tideturner: You reveal your hidden Tideturner at a battlefield. This places the Tideturner's "When you play me" (WYPM) trigger on the chain.
3. Tideturner's trigger resolves: The Tideturner swaps locations with the unit at your base.
4. Bellows Breath resolves: When Bellows Breath resolves, it tracks the original target to its new location at the battlefield and deals damage.

Note: I could not fully verify this ruling against the retrieved rules.