The more I watch these scenes, I don't think Fredo could have tipped off Roth. Immediately preceding Bussetta's attempt on Roth at the hospital, there's a scene from the party:

- A Senator makes a comment that he thought Roth would be in attendance. Geary asks about protocol.
- Presumably senior Cuban military officials march into the party and talk to Batista behind closed doors. Michael astutely observes this while eating cake.

This is speculation, but I would agree with Turnbull's take -- Batista was advised of the rebel situation, realized his situation was untenable, then ordered the military to provide protection for his supporter Roth (Roth was based on Meyer Lansky, who contributed millions to Batista's fortune). Having come across Ola's body at the hotel, the urgent march to the hospital and shooting of Bussetta would make sense. In the follow up scene in Las Vegas, Tom Hagen notes that Roth was moved to Miami. In real life, most of Cuba's government, friends and supporters left the island before sunrise, and Castro didn't capture the city until January 8.

Michael had already made his own plans to depart. Before giving the kiss of death, he told Fredo he had a plane leaving in an hour. As Batista announced his resignation, Michael started making his way off the island. One could assume that the money and his belongings were awaiting him in the car or in the plane.

Something else I noticed while catching the end of GF1 yesterday -- just before Vito's death, he and Michael lay the groundwork for the climax. Vito reminds Michael about monitoring the inbound and outbound calls to root out the traitor.

Considering that, plus Paulie's treason was earlier exposed the same way, I would suspect Michael would have performed the same measures after his assassination attempt. Ola's middle of the night call to Fredo would have raised Michael's suspicion that Fredo was the one who flipped, and the Havana trip was to fully flesh that out. With the Corelone family all located in the Tahoe compound, that monitoring would be easier. Granted, there wasn't caller ID in 1958, but a long distance call from Miami wouldn't be too hard to figure out.