Coach situation

High school teams here are allowed to scrimmage during June. I was working the semifinal of a tournament with pretty big schools. Game is going well when my partner (Lead and a veteran official) makes a tough block/charge call during transition. He calls a charge on A1. I am Trail tableside right next to Coach A (in his 43rd year coaching). Coach A goes nuts yelling about how that was a terrible call. He's yelling at my partner but I am right there. I was at his side right after he started yelling and was talking to him saying "coach stop, coach calm down, etc". He had been good so far in the game, hadn't been an ass, so I wanted to give him a chance to calm down.

He didn't take that chance, so I turned away and called a tech. I immediately walk away from him as he starts to realize what I've done. I walk towards the C and meet him at halfcourt. I tell him I've called a tech, etc., etc. Meanwhile Coach A has stopped yelling at Lead for the call and is now yelling at me. "What did I do to you?!? I was yelling at him!" I could have given him a second but (wisely I think) chose not to.

Later in the game I was Trail during FT's and talked to him for a minute. I mostly listened and let him vent a little. No surprise he didn't think he deserved that one.

My questions: should I have let my partner who made the call deal with the yelling and call the tech? Do I have a responsibility being tableside right there to call the tech to back up my P? If warranted, should I call the second tech or let a partner get it? This is summer league ball and I didn't think it was the right environment to run him by myself.