Rubio was born in Miami, Florida, the second son and third child of Mario Rubio y Reina and Oriales (née Garcia) Rubio. His parents were Cubans who immigrated to the United States in 1956, prior to the rise of Fidel Castro in January 1959. His mother made at least four trips back after Castros victory, including for a month in 1961. Ultimately, his parents applied for U.S. citizenship and were naturalized in 1975.
Kind of a gray area since his parents came here in 1956 and stayed. I assume they had legal visa status though..