It rains every day somewhere in the Caribbean. This is common and not dependent on the time of the year. The good news is it usually doesn't last long. I don't think I've ever been on a Caribbean cruise where the ship didn't encounter at least one or two rain showers during the cruise. Same goes for the ports. Humidity is typically higher towards July and August, and then more so in the western Caribbean. The eastern islands (St. Thomas, etc.) are usually less humid. Cozumel can be killer in the dead of summer.
When you go to any particular island doesn't matter. There isn't anything that makes XYZ island more attractive in May than any other time of the year.