The "surplus EXP" isn't actually put towards anything at the moment. You can't spend it anywhere and it doesn't go towards anything, though SE made some comment about how it was an interesting concept.
They suggest switching your classes, I suppose, so that you are always getting 100% returns for your time instead of slogging through the EXP cuts.
The surplus EXP does go towards BOTH kinds of EXP. Class level and Physical level are separate entities. Physical level follows you no matter what class you're on, Class level only matters when you're on that specific class. Since physical level affects EVERY class you play, its cooldown is shared through all classes. Class level is based on your class only and the surplus from your Pugilist doesn't affect your Lancer (for example). It's your Class level that determines your abilities and the level of the mobs you fight (from what I understand). Your physical level has more to do with your stat allocation (again, from what I understand), and actually has very little effect on beta players from what I've heard.