The wire grill they set the cup on is at an angle. Setting the cup there leans it against a lever. When the lever is depressed, soda starts flowing. Here's the neat part: based on how much the lever has been pressed, the machine knows what size the cup is (it's a long lever). It then fills it most of the way, waits a bit for the fizz to settle, fills it a little bit more, waits a little bit more, then fills it again. A perfect cup of soda, and the person expediting the order can do other things while the cup is filling.
I imagine it requires the person to fill the drink with the right amount of ice. I wonder what they do when the person requests no ice. There didn't seem to be any manual override for this. I'm tempted to go there and ask for a soda with no ice just to see what happens.