Possible dropped 3rd strike mechanics

[Little Jimmy]

Same C ball weekend. I'm working with a new ump. He's plate. 2 outs. Runner on 3rd. Batter swings at a ball that bounces in the dirt into the catchers glove. Plate says strike three (not an out call). Batter walks toward dugout, not attempting to go to first. Offensive coach says he thinks there's only 2 strikes. Partner asks me. I say I only have 2. I come to him (watching BR who is still standing close to out of play). He asks what to do and I say you need to ask both coaches. One coach has 3. One has 2. They continue to talk on the field with BR still very close to out of play. After a moment he declares "that was strike 3". BR then walks into dugout. 3rd out recorded. Inning over.

My thoughts were...
-No time was ever called. Correct? We had to give the BR and the runner at 3rd a chance to advance if it was strike 3. With plate ump and both coaches on the field, what could have happened if BR did go to 1st or if runner on 3rd broke for home? Potential coaches interference somewhere? There was no complaints from the offensive side, but I wondered about the mechanics.