I do not believe there was any conflict at all between the two. Not to mention the fact that Tramunti was gonna be buried under 15 years anyway, so what conflict ya know?
Corallo assumed the boss position when paroled because I do think that was the plan.

If there was any conflict at all, it was that Tommy Pappadio didn't wanna step aside as the "acting boss" Corallo, so he got hit in the head. But between Tramunti and Corallo I think it was fine IMO.

At least that's my theory on it.