if my opponent moonfalls my unit from a battlefield i control to on they control, could i then reveal a hidden tideturner to move that unit back?

It depends on whether you still control the battlefield where the Tideturner is hidden.

If that Moonfalled unit was your only unit there: no. When it leaves, the following cleanup makes you lose control of that battlefield (Open state, no units there), and the hidden Tideturner is trashed in that same cleanup — there's no priority window to play it in between. This is the same result as Charm or Blitzcrank moving your only unit away (FAQ 1943, FAQ 8081).

If you kept another unit there, there's still no window right after Moonfall resolves — the chain is empty on your opponent's turn, and in Neutral Open only the turn player can act. But your unit landing on their battlefield applies Contested and opens a Showdown there. During that Showdown — and since your unit applied the Contested status, you gain Focus first (Rule 345) — you can play the hidden Tideturner as a Reaction. Its errata lets it target a unit you control "at another location" (Rule 811.1.d.2), so it swaps with your unit and brings it back; Tideturner takes its place on their battlefield (FAQ 1652, FAQ 281).

Note: playing Tideturner in response to Moonfall while it's on the chain won't save the unit — Tideturner enters at the same battlefield as the target, so there's no "another location" to swap with, and Moonfall still moves the targeted unit.