The reason many people left was because Fidel Castro left the people oppressed, poor, and hungry. After he was done with them, they had no money (because he had changed the money currency so the money they had was worthless), and everyone worked for the government under harsh conditions.
Cuba does not have a prime minister as such. The official position of Prime Minister was abolished in 1976, and replaced by the position of President of the Council of Ministers. The last prime minister was Fidel Castro , who assumed the new position. The current council president is his brother, Raúl Castro , who is concurrently the First Secretary of the Communist Party in Cuba.