What happened is that a week or so before my flight, the Cuban government changed their regulations regarding the tourist card. The norm before is that you only needed to get one at the airline counter right before your flight. The rule change came in the form of a list of countries that are no longer eligible for that, and that list includes the Philippines. Basically, you are still getting the same tourist card, but with the seal of the Cuban embassy at the back. In my case, it was the Cuban embassy in Mexico City.
Getting the visa from the embassy did not take more than 20 minutes. I had to pay a fee of around MXN450 (~USD25) for it. The requirements included a copy of the front page of my passport, as well that of my roundtrip ticket. I was supposed to fly to Havana in May, but I had to rebook everything because of this. Had I checked beforehand, I could have saved a couple of hundred dollars. Whatever. I hate visas, seriously. FYI, I’m in Mexico on a tourist visa, but the Cuban embassy still entertained me anyway.