Yes, They were born and lived their lives in Cuba.
We, are the first generation to come to the U.S..
We immigrated in 1967, I was born in Cuba and was only two years old when we arrived in the U.S.
Good luck in your search.Maybe soon we can FREELY go back to Cuba and be allowed to do some great research.
That is if the records are still around.I have heard that many records were destroyed so that in the event that Cuba would be freed from you know who, it would be difficult for Cuban Americans here in the U.S. to make claims on properties that they left in the 1950's and 60's.