[commish]

It is the umps responsibility to call the managers for a sidebar in that situation and say 'here's what happened now forget it and play ball.'

And that is exactly what happened. Per the AP article on the incident :

The flurry of between-innings meetings started after the first inning, when the umpires and La Russa talked out by first base.

Then, after the top of the second, Rogers was greeted by plate ump Alfonso Marquez as he walked off the field toward the dugout, and the two of them chatted for a full minute. Then Leyland came out of the dugout and he and the umpires spoke.

Then, after the bottom of the second, Marquez went over to the crowd and spoke with Steve Palermo, an umpire supervisor who was sitting in the front row next to the Detroit dugout.

[Rippin]

With televeision coverage I can't say for sure, but it sure look liked the umps were having a series of meetings and never put a sharp end to with the managers.