Vito had made it clear that Sonny would succeed him. Michael "made his bones" by whacking Sol and Mac. After Sonny died, Vito made it clear that Michael would succeed him--in fact, Michael had already succeeded him before he died. Sure, some of the made men might have resented Michael--human nature. But, I think Tessio never expected to succeed Vito. He betrayed Michael because he thought Michael was too weak to confront Barzini, who was encroaching on Tess's territories. But, perhaps Barzini promised Tess that he'd be the new Corleone Don after Michael was whacked.