Can opponent Rengar ambush as a reaction to a spell play on my turn?

Yes. Ambush grants [Reaction] while playing to a battlefield where you control units, and Reaction can be played during a Closed State on any player's turn — so your opponent can Ambush Rengar in response to your spell on your turn (Rule 813.1.c.1, Rule 822.1.b).

Two conditions apply: they must have a legal location and be able to pay the cost. A standard Ambush unit needs a battlefield where they already control units; Rengar, Trophy Hunter can instead use his special ability to Ambush to a battlefield where there are enemy units even if he has none there. Rengar, Pouncing is different — he has [Reaction] printed but no Ambush, so he'd need to go to your Base, a battlefield you control, or a battlefield you're attacking.

One more note: since your spell play creates a Closed State (not a Showdown), only Reaction-timing cards can be played — a plain [Action] unit or spell wouldn't work there.