Well, my house rules would say that since he showed his cards as a misunderstanding, you cannot increase the betting, but you play the hand as all in.

However, that is not the question.

You have JJ, you put $1.50 into the pot...
He shows A2 then raises another $.50
Did you make the right move to call?

Yes.

I'm sure JJ is a big favorite to A2, and you knew what he had. I can't see anyone folding a $.50 bet in a $4 pot with a superior hand.