Will the inmigration agent of Cuba stamp the passport to the EEUU turist ?
Generally, the inmigration oficial DON’T stamp the northamerican pasaport; in this case they must stamp another document separately, and you must keep it with you at all time that you will be in Cuba. Other option is to come to Cuba with the passport and your Certificate of Birthday. In the case (less probable) that your passport was stamped, (if You come back via Mexico) Its possible to use your Certificate or Birthday to get back to United States.