It's determined by umpire's discretion. He or she has to determine the legality of the play. Based on the fact that the umpire called the runner out makes me believe the play was legal. Without video evidence no one here can make an informed decision, and even video might not give difinitive proof.
Taking the OP's account of the event and the fact the batter was called out I think we can all make a pretty informed decision.
Now it's right.
Not really. Were you there? Did you see exactly what happened? Did you hear the other half of the story? The other coach was arguing....and he was there. This type of play is a judgement call by the umpire, and since we were not there we cannot make an informed decision. We can make a "best guess" decision but not an informed decision. We only have a little more than half of the information. I "believed" the umpire in my prior post.