Time out or foul?

[chymechowder]

Had a situation in a JV G game tonight. Only the third HS game I've done. Not sure if I did this right:

After grabbing a defensive rebound A1 has the ball. B1 and B2 converge on her. I'm the new trail; the play is right in front of me.

A1 can't find an outlet pass. I hear a "time out!" from the bench behind me, but don't process it right away as coming from the coach. Immediately thereafter, and in bang-bang fashion, there's a second time out call as well as a foul by B2 on A1. My fist goes up for the foul--just as I realize that the coach had called timeout. (D'oh!)

I say "No foul. Time out Red."

Coach says, "It shouldn't be a timeout. You called a foul, right?"

I say, "Yes. But it was a split second after I registered your request for time. You had possession and you called for time. I should've granted the timeout first."

My partner came over and backed me up, saying that he had the time out, too.

She was reasonably ok with the explanation, but is that right? If it happens quickly enough, can we retroactively grant time and "wave off" a common foul or violation that occurs in the time it takes for the (admittedly green) official to process the TO request?

(And hypothetical: say the foul had been for someone throwing a punch. Would we still grant the time out, and then treat the punch as a dead ball technical?)