An even simpler answer: directoral license. It was convenient for Puzo and FFC to have Vito make those predictions in order to set us up for the denouement--especially that nice scene where Tessio lights Barzini's cigarette and makes his pitch to Michael.

Closer to logic: Barzini had been signaling bad intentions by crowding the Corleones (as in Tessio's beef in the fishtank scene). And, Barzini knew that the Corleones' move to Nevada would still leave a Corleone family, allied with Michael, in NY, and still rivaling Barzini's family. So, I don't think Vito was being overly prescient in his predictions. And, as Lilo said, in the Mob, it's always your friends who do you dirty.

What really puzzles me is why Vito didn't know, until after the Commission meeting, that it was Barzini all along. "Tattaglia is a pimp - alone he could never have outfought Santino." Sure, Vito - and that was true before the Commission meeting.