Castro took over Cuba in 1959 after a guerrilla insurgency begun in December 1956. Marco Rubio's parents left Cuba in 1956, according to this story in the Tampa Bay Times:
'To press their case, birthers dug up Rubio’s parents' immigration papers. While the eligibility question is unresolved, in some eyes, the file (which the Times independently obtained) confirmed his parents were given citizenship in 1975. Rubio at the time said he did not know why his parents waited, though experts told the Times that it wasn’t uncommon for some immigrants to wait.
'The immigration dossier broke some news: It showed Rubio’s parents came to the United States in 1956, not after Fidel Castro took over, as Rubio’s ... official biography noted and he repeatedly implied when talking about his “exile” parents.'
In yesterday's Republican debate in South Carolina, Rubio similarly misrepresented himself on a number of issues.