This Movie Got It Wrong
The end of the movie shows Castro's Rebels taking over the country and everyone leaving Cuba ASAP.
In reality, the USA doomed Dictator Batista by not giving him the military weapons he asked for in March 1958. When Castro took over New Years Day 1959, he visited New York was hailed as a hero in the USA. Many Americans continued to live in Cuba for at least a year under Castro. When he began nationalizing American owned businesses, the USA retaliated by placing embargos on certain trade goods. Castro stepped up his nationalizations and that's when Americans left, since they no longer had jobs.
The USA closed it's embassy in Havana in Jan. 1961, just before the inauguration of Kennedy.
In April 1961, President Kennedy gave the green light to a CIA backed invasion of Cuba which had been planned by President Eisenhower in 1960.
The invasion (Bay Of Pigs) failed and probably persuaded Castro to get Soviet Missles intalled in Cuba against future invasions.