When I used to coach, I always used my full 30 seconds too. I would get my player ready and talk to him while walking him to the table. I kinda had it down timing wise perfectly. As far as the T goes - it seems a bit hasty. It sounds like younger officials who put the ball down on an oob even though the team is walking across the floor.
AS far as you sitting - you weren't ejected. Usually that is due to an ejection . . . again, since it was a freshman game it's possible the second T won't even be reported. I know of some officials that don't report T's like that . . .
