I just wanted to add a few things on my experience. When I did the technical stop at TAO, I had the blue card filled out. When I got to immigration, the officer asked me if I want to enter with the visa instead, so I did. I didn't really know what to do. He was going to give me the option to get the free visa.
I only bring that up, because there was another American, who had the same flight itinerary as me. She did NOT have a visa. She was able to pass immigration with a free visa. We're both about to board to Korea in a bit.
So she was able to transit through TAO to XMN perfectly fine on the free visa. I'm not sure if it was the 24 or 72 she was on, that she got from TAO immigration.