If it is an assassin, then:

1) Who is his employer?
2) The answer is most likely New York. But then:
3) Phil's dead. Butchie made the truce with Tony.
4) Why would Butchie kill Tony? It doesn't make sense; without the direction of Phil (or the direction of Tony), the two families wouldn't have much business to attend to.
5) Is it possible that the Members Only guy was employed by Phil, and when Phil was killed, word couldn't get to Members Only? It's possible, but unlikely.

The last scene is at once relieving and tense. With Phil gone and the NY/NJ war over, he has every reason to sit down and enjoy a meal out with his family. On the other hand, his shrink has left him, his son just tried to commit suicide (and previous plotlines tell us he's prone to recurring depression), and Carlo just flipped to the Feds. Indictments are on the way.

The scene mirrors not so much Tony's paranoia, but his need to be paranoid. He can't live comfortably, he can't afford to. All this wealth and prosperity has brought him to a miserable, wretched life, with only surface grins and warmth.