My opponent has one unit at a battlefield and hidden card (tideturner). I have one unit in base and I play void assault, moving my unit from base to battlefield and opponent's unit to his base. Does he have to flip hidden tideturner in response to the void assault or can he do it after void assault resolves, so he can swap places with the unit in his base?

He can do it after Void Assault resolves — he doesn't need to (and actually can't meaningfully) respond to the spell itself.

If he plays Tideturner while Void Assault is still on the chain, his unit is still at the same battlefield, so there's no "unit you control at another location" for the swap to target — Tideturner would enter, do nothing, and then Void Assault moves his unit to base anyway, stranding Tideturner. Instead, once Void Assault resolves, his unit is in base, your unit Contests the battlefield, and a Showdown opens. Because the battlefield is Contested, he keeps control of it and his hidden card stays until the Showdown completes (FAQ 8081), so when Focus passes to him during the Showdown he can play Tideturner for [0]; its "another location" targeting bypasses the normal hidden-target restriction (Tideturner errata, Rule 811.1.d.2), and the swap puts his unit back at the battlefield to defend.