OK, first off the pitcher is in contact with the "pitcher's plate" or the rubber. There's no "bag" there.
Second, I don't know "utripp" rules, but I'm surmising that like a lot of league rules it's OBR with some safety modifications. If that's right:
Once the pitcher has come set, he can legally do only 3 things:
1. pitch to the batter
2. step and throw (or feint) to a base
3. legally disengage ("step off")
I can't follow your argument. At one point it sounds as if you said the pitcher didn't step ahead of the throw (you allow "b-he has to step towards the base in which he's throwing to."). If that's what you called, then you were correct: balk. All you have to say is "Coach, no step." If he doesn't know what that means, you can add "he has to step toward the base to which he's throwing."
On the other hand, you seem to have insisted to the coach that he had to step off first before throwing to a base ("I told him that he has to step off the bag first before he does anything"). That's wrong. The pitcher can step toward a base and throw directly from the rubber. In OBR he can do that from either the windup or the set position.
The relevant OBR rule is 8.05. You might wish to purchase a manual like the Jaksa/Roder manual, which does a terrific job explaining the rules. Here's a
link to it.