I couldn't figure out from the video at what stage and how is the liquid and the carbonation placed inside. I assume it must be just before putting the lid on, but I don't see how the lid is put on if the contents are generating outward pressure.
If you put a sealed lid on the cup, the pressure will build up inside the cup as some CO2 comes out of the liquid into the top of the cup, till there is an equilibrium and no more gas comes out.
Thats what the canning process relies on. So the can isn't sealed under pressure - the can is sealed at room pressure, and then within a few minutes the pressure builds up inside the can.
Kinda neat!