Can't find it in the rule book - Help

[Wellmer]

A situation happened in a game last night that I worked and a fellow official disagreed with my assessment of the rule. I could not locate it in the rule book to backup what I thought was the correct ruling. Here it is.

Visiting team calls a time out as the Home team is preparing to shoot two free throws. After the 15 second warning buzzer sounds, a member of the visiting team checks in at the table. We correctly do not allow her to enter the game at this point. This is where the disagreement takes place. I say she can enter after the ball becomes alive, namely after the first free throw is attempted. My partner says that since she wasn't there before the 15 second warning buzzer, she cannot enter until the after the clock starts. I told him he is getting that confused with a player that has been subbed for and then wishes to reenter. She is not allowed to until the clock has started, then she can go to the table to reenter. I cannot locate the rule that says this sub can enter the game after the ball becomes alive, namely after the first free throw. Someone tell me where its located in the rule book, case book, etc. This is NFHS rules if that matters.