You are right with normal capacitors. The voltage rating is the voltage which, if you exceed it, they run the risk of exploding and filling the room with a horrible acrid smell, and showering the place with electrolyte (note: you have to exceed it by quite a lot to make this happen, but it is fun when you do
- normally they just vent and stop working right).
Supercaps work just the same way, but I would imagine the bang might be bigger - maybe I should try it some time
You can operate at any voltage up to the maximum, and that is the voltage they give you. (n.b.: that is my personal interpretation of the Wikipedia page