Subbing during FTAs

[Amesman]

Granted, sometimes underlevels especially get loose with reporting subs to the table in a timely manner. But I have to know:

Last night, as T, I disallowed a sub after a made FTA because I felt the coach ran her to the table too late. I felt the sub should have been there by the time I checked the table after the first FTA was converted.

So my question is does 3-3-1c mean that if I check the table for a sub waiting to come in after the first FTA is made and nobody's there, I need to let the sub in anyway if the table buzzes after the 2nd FTA is made? I'm not turning around again to see if someone's at the table while the teams are starting to hustle down the court after the made 2nd FTA.

I realize the scoreboard operator doesn't dictate when subs come in, but his buzzer did stop play before the ball was subsequently inbounded ... And now I realize that one way or another, I probably did commit an error by not allowing the sub in once play was stopped. Or did I? Coach was pretty sarcastic a little while later when he asked if, during a TO, he could sub her in now.

And here I was, feeling pretty good about what I thought was a not-too-bad game last night ...