It turns out the ump was talking to the guy who plays the music over the public address system. That's who was being ejected.
Apparently, umpires don't like it when the music guy plays "Three Blind Mice" -- especially at a time when the manager of the home team is on the field arguing that they didn't see a play correctly.
According to the local paper, the public address system at the stadium was shut down for the rest of the game. So, fans took it upon themselves to announce the names of players as they approached the plate.