He didn't go to Cuba expecting Roth to tell him who was the traitor in his family. He went because he needed to get away from Tahoe, for the safety of his family and himself:

The Tahoe shooting proved two things: First: Although Michael was the target, Roth was ruthless enough to have his bedroom sprayed by machine gun bullets--and too bad if Kay was collateral damage. Second: there was a traitor "very close" to him. If he remained in Tahoe, he'd still be a target, and his family would still be in danger. By taking himself away from Tahoe, he was removing the target from his family. And, as long as Roth was greedy for the $2 million, Michael could buy time to find out who was the traitor.

I don't know how he thought that being in Cuba would bring him closer to finding the identity of the traitor. But it was certain that he wouldn't find the answer by remaining in Tahoe--all he'd find was mortal danger to his family and himself.