Paul had a problem that went beyond Tommies actions in the Batt's incident. Burke and Hill were also involved. Paulie had several options. Do nothing and let the Gambino
Family respond as they saw fit. If this occured all three men would more than likely get hit. Or paul could sacrifice Tommy in hopes of making peace with the Gambino Family. In doing so he could potentially save Burke and Hill who were at the time one of Paul's best earners. That is why Paulie hit Tommy D. But above all Paulie knew if he did nothing the Gambino Crew would. None of these three men were made. So The Gambino Crew could kill all three and Paulie could do nothing.

Because Tommy Whacked a made man without the families permission.Thats a no no..

Also paulie must have gave the gambinos some kind of compansation for batts,a piece of Action etc