When I flew Southwest back in May, they asked me at the counter when checking in for my reason for travel. (we weren't checking bags). When we got to our stopover (before cuba) that is where we had to purchase the "visa" before we boarded the next plane. My passport was NOT stamped and did NOT say anything to the agent about it (since it was legal for US citizens to travel there). They stamped my "visa" that I purchased in FL though before leaving cuba.