Ok, now I have definitely had that issue before. Basically exactly how you described. I replaced only the radiator and had no more issues. Your thermostat is probably ok, but they are so cheap I wouldn't recommend not replacing it also. I think the water in the rad turned to straight steam because it's not under any pressure if it's steaming out like that, plus you may have needed more than a gallon if the water that normally sits in the block was also gone. With only a partial fill, it will turn to steam faster and steam out of the gap quicker.
Picking up the T-Stat, gasket & new cap from NAPA after work. KIA dealer would had to order the T-Stat & gasket. I don't have time to wait.
New radiator should be here Friday from Rock Auto. I wanted an all aluminum but the place I was looking at was out of stock. I need my Sporty up & running this weekend.
Didn't think about the block being low or empty or plain water having a lower boiling point.
Last thing I might need is a gallon of coolant. I have about 1-1/2 to 1-3/4 50/50 at home. I buy a gallon of straight and a gallon of distilled water and mix myself. Much cheaper that way.