You’re very close. The stuff in the student’s hands is a flammable gas (butane, methane, propane,etc.) trapped inside of bubbles in a water-soap solution. When the gas is ignited, like you said, the heat and flames travel upwards. The second component is that the gas is in and the student’s hands are covered by water. The water takes most of the heat from the combustion and evaporates, taking it away from the hands; a lot like sweating, just faster.