I live in Florida and own three Cubans. the only thing I've ever heard or read about them being illegal is that it is illegal to catch one and then release it. Once you've got your hands on it you're NOT supposed to let it go. You're supposed to humanely euthanize it.
Which is why I've got three. Because instead of euthanizing them I keep them.

I did hear (from Tommyboy on FF) that you have to have a license to transport or ship them out of state. Even to state where they would not be able to survive in the wild.