Overacting cores would be generating too much power, or power that outputs inconsistency. For instance, a fire core for a stove might have the stove work at too high a temperature, turn on or off without the owner knowing, or flare up. The emotions are used to re-start them, and there is not one emotion that works for all elemental cores, so you can use any emotions you want. It's just that some emotions will work better with one core than others. What they're looking for is a steady flow of emotions to ease out the unstable kinks that these cores are having. How long that takes depends on the character (or how long YOU want your character to fix them).