I have been to Cuba but only in October, but I have been to other parts of the Caribbean in September and the climate is similar. The weather is usually good sunny and hot, if it does rain it will be for 30 mins and very heavy. then clears up sun is back out. but I have had 2-3 days of constant rain when we had a tropical depression. It doesn't happen too often but it can, its the tropics you have to expect some rain during a 2 week holiday.