I don't think you're thinking about this correctly... if they are infected, they will pass the disease (through mosquitoes) along until the next bunch is ready to fly south.
Castro's scientists have been studying how to transmit deadly pathogens using migratory birds since at least the mid-80s. They've had plenty of time to work out the logistical problems or develop antitoxins. Are you suggesting this isn't true or that Castro would be deterred by the risk of infecting some of his own people? Using that logic, terrorists would never hijack planes and fly them into the World Trade Center? After all, they would be killed too.