I've tried to think of a connection between Eugene Pontecorvo wearing a Members Only jacket in the first episode of 6-pt 1, and Tony getting it from the guy in the Members Only jacket at the end, but I've come up short.

But you have to ask: Who would have the balls, and the muscle to deal with the fallout, to whack a boss, even a Jersey boss? It had to be the New York Lupertazzi Family. The assassination was professionally done, that's unquestionable. It wasn't just some emotionally motivated killing.
And Butch was probably getting a lot of pressure from his Capos to revenge Phil's gruesome death, however unintentional it might have been. That could have been enough to make him finish what they started by chopping off the head and doing business with whatever's left.