I think I was more surprised that Girardi was that fired up; I thought all the Yankees management hated A-Rod. Brian Cashman was probably p---ed that Dempster didn't aim higher.
There is a difference between the team and the organization. ARod (and his camp) and the Yankees organization have beef. I believe the Yankees are in the wrong. They knew he was on something, and still gave him an even larger contract than his previous one. Once he stopped putting up MVP numbers, they turn their backs on him. I think they intentionally kept him out this year longer than necessary (hoping a suspension would kick in), possibly purposely messed up his diagnosis last year, and potentially had something to do with the investigation.
That said, I don't think any of that spills over into the clubhouse. I'm glad Girardi did what he did and it definitely didn't appear to be an act, especially given his post game comments after a few hours to calm down.
By allowing that to happen (by not ejecting Dempster), they should have also allowed CC to retaliate, but it was very poorly handled by the ump. Any time you throw behind a player it should raise an eyebrow.
I'd be surprised if the Yankees don't drill someone (preferably Ortiz) next series.