I've read a number of articles on this. Cubans are not fleeing to Costa Rica in an attempt to reach the US. However, the problem with this article is that, while it talks about the problems caused by this, it doesn't answer the question of Why.
Read more @ ‘Costa Rica faced by mass migration of Cubans trying to reach the U.S.’
Read more @ ‘Costa Rica faced by mass migration of Cubans trying to reach the U.S.’