I think it was an example of Vito's "Sicilian cunning" at work. He made the other Dons believe he was weak and fading, and he and Michael were conspiring to make them think Michael wasn't the man Vito had been. And Vito had already concluded that "it was Barzini all along." So, it was logical for Vito to conclude that Barzini would make the next move--and do it by getting a trusted Corleone higher-up to turn traitor.

BTW: Another measure of Tom's lack of Sicilian cunning, IMO, is his statement, "I always thought it would be Clemenza." Why? Clemenza never evinced a shred of disloyalty to either Vito or Michael. Michael's reply, "Tessio was always smarter," was the logical (or if you like, Sicilian) conclusion.