Yes, it usually rains every afternoon in Florida in the summer, but the rain doesn't last long and can be a welcome sight in the humidity!
When I lived in Ft. Myers we could always tell the tourists from the residents when the afternoon showers hit...residents ignored it and tourists grabbed everything and ran around like chickens with their heads cut off, trying to make it back to their cars!
Like others have said, bring a poncho and keep on enjoying Disney!