Villain 1 should have repotted on the flop, and probably given some thought to folding on the turn. With a rainbow flop Villain 1 has to know he's up against at least one and perhaps two opponents with straight draws.

I probably would not push on the flop, but it's a close decision. If Villain 2 had a bigger stack and would stay in, I might push. I would call Villain 1's bet on the turn and/or bet (as you did) regardless of what card comes if the board doesn't pair. Otherwise the play is fine.