What is a draw

I had a game recently in which I had a king, a rook and a pawn, while my opponent remained with only a king and a pawn. Clearly a winning position.
Unfortunately I was running out of time, had only 4 seconds left. I sacrificed the rook killing the opponent's pawn, so the opponent had only the king, therefore ending the game with a draw instead of loosing to a clock. If I had enough time left, I would lead this to a checkmate with no problems.

My question is: was that necessary? If I ran out of time and the opponent still had that pawn, would it be considered an "insufficient material"?

No. You would have lost, since the pawn can be promoted.

You made the right choice, you would have lost

There is a nonzero chance they can still win if they promote the pawn sonehow. As long as there us a nonzero chance, they can't tie on insufficient material