Why mechanics would have mattered.....

[Chess Ref]

My partner and I are wrapping a BJV game. There is 11 seconds left in game. Visitors winning by 12. I am trail. Partner has a foul on home team. I move under basket lining them up for the free throws. Lined up , partner done reporting and horn sounds. Player has 5 fouls. Partner runs over to player who is standing by coach and informs player and coach he has 5 fouls.
We all stand around for about 45 seconds and partner goes back to trail position. I look at him and they say "what's up" . They still hadn't replaced disqualified player. Partner informs me coach is being belligerent and I should go ahead and administer the free throws. I give the ball to the shooter-he shoots-partner tweets and calls a technical foul on coach for not replacing player. I now switch with partner so I can deal with the home coach. They inform me my partner never told timer to start the 30 second clock-so they were not required to have a substitute ready. hence they believed there should be no technical foul.

So my questions are

1. I should have notified the coach/player of the 5 fouls ?
2. I looked everywhere for where it says there has to be an "official" countdown of the 30 seconds . Couldn't find it. I did find in the officials manual that the timer sounds a horn at the 20 second mark-but not much else. Anyone point me in the right direction concerning an official countdown ?

Sidebar-I find out afterwards partner had never had a player foul out before so he thought because he was the new trail he was suppose to-hence his running over and doing it. And my bad for looking at the clock and thinking come on coach send kid in and lets go home.