We've had several threads here on why Michael made Carlo identify Barzini as the one who approached him about setting up Sonny. Some here think it was a final test for Carlo; others believe that, maybe, Michael needed "justification" from Carlo's lips before whacking him.
In a parallel vein: Before Vito died, he warned Michael: "Whoever comes to you with this Barzini meeting, he's the traitor." Sure enough, Tessio proposed the meeting at Vito's burial. From that moment on, there was no doubt in Michael's or Tom's minds that Tessio was a traitor. BUT...
Is it possible that, when Cicci said, "Sal, Tom, the boss says for you to go on ahead and he'll come later," he was really expressing Michael's final test for Tessio? If Tessio had said, "Sure, ok, we'll catch up," then maybe Michael would have had doubts about Tessio's guilt. On the other hand, when Tessio replied, "Hell, he can't do that, it screws up all my plans," it was final confirmation of his guilt. What do you think?
I don't buy either. Michael was simply enjoying toying with Carlo. That's all it was. He was the shark circling his prey. Remember when Vito put Bonasera through that grueling "you don't even call me Godfather" song and dance. Well, Michael's getting Carlo to admit his guilt was a form of that same thing.
As far as Tessio goes, it was just a way to make the scene more dramatic.