I agree with everything you said. It’s fall ball, but the umps in this situation are the ones who typically call spring/summer tournaments as well. They do rec and travel. Just from my baseball days, I know an ump has to acknowledge/confirm my request for time before I can proceed, in any capacity, on the field of play. The coach that committed the interference apologized and verbally expressed that he knew he messed up. When I told the field ump about the interference, he claimed no such rule exists, so my assistant said, “So, it’s okay for me to walk on the field at any given time and loudly yell “TIME” while a ball is live and I’ve not broken any rules?” The umpire replied, “It would be a problem, but she still left early, so it’s an out”, then proceeded to jog back to his field placement for the next batter, lol.And by "authorities" we are referring to the coach who walked out on the field and "called time," right?
I don't know the situation of umpires in the OP's league, but I will venture on the side of "two umpires on a 10u softball game in September" are probably not sharpening their skills while waiting for MLB postseason assignments in October. But, that is our expectation ... while Coach Doofenschmirtz, the infallible professional, creates a train wreck.
While we hope that umpires would know the coach cannot call time out (he can request it) and would properly assess the penalty for the verbal interference he committed (yes, it was interference in ANY code by the OP's description ), I would also say you need to look at the scenario and all the culpable parties. Want them to get it right next time? Train the coach not to commit interference and then train the umpires. Just 'cause you gave them indicators, a shirt, and maybe a free hot dog does not make them umpires. It makes them two guys (or gals) trying to do some good for the youth in their community.