I can't remember exactly when this started, but I think it was under either Carter or Clinton. At any rate, while they said it was to discourage Cubans from attempting a risky voyage, it was really to suck up to Fidel.
I've never heard the notion that Cuba was still an American Protectorate after Fidel seized power.
Not that that applies to Rubio as his parents were born before Fidel came to power.