What is the reason for this route while flying from USA over Cuba? I was flying from Canada to Jamaica, and just past Florida the plane turned 90 degrees towards Nassau. It then continued over Cuba. Is this because of the situation between Cuba and the United States? It appears the plane must enter Cuban airspace from international airspace. But I have heard some planes can enter Cuba via corridors from the US. I am confused over this situation.

This was flight TS0373 on 17Jan2016.
There are two large warning areas there, W-465 A and B. Both are active "intermittently" up to 70,000ft. It seems likely that the route was taken to avoid those areas.