opponent played ride the wind to move his tideturner from his base to my battlefield with trophy hunter rengar. can he still followup with another spell "switcheroo" that is action speed too? i dont have any other spells to react to

Yes — he can play Switcheroo, but only after Ride the Wind resolves, and you get the first window before he does.

Timing: he can't stack Switcheroo on top of Ride the Wind expecting it to work afterwards — the newest chain item resolves first, and while Ride the Wind is still on the chain Tideturner is at his base, so there aren't two units at the same battlefield to swap (illegal targets). Once Ride the Wind resolves, Tideturner lands at your Rengar's battlefield, the showdown is still open (no combat damage until both players pass), and when his chain empties focus passes to you. You pass, he regains focus, and Switcheroo is legal — Action timing works in a showdown (Rule 347.1).

What it does: swapping Might in the same battlefield makes Rengar 2 and Tideturner 6 for the turn, which matters for the combat damage step that follows. If you have nothing to play, him "following up" is entirely normal — but he has to wait for your pass rather than playing it over the top of Ride the Wind.