Low fertility affects populations, but slowly, because people live for 80 years or so.
Cuba doesn’t have a fertility problem, it has a “I don’t want to live here any more” problem. There can be a snowball effect – the more of your relatives have fled to Florida, the more appealing it becomes to go yourself. Because normally family (and jobs and friends) is what keeps people from fleeing.
Sorry, it does also have a problem with the fertility rate being only 1.4. That could be due to fertile people being the most likely to leave. Over 65s are the only age category that is growing in numbers in Cuba.
Over 850,000 people have fled Cuba for the United States in the last 3 years, reports the Latin Times. For a country with only 11 million people, that is highly significant