Well, they know about days. That some 365 (or whatever number) of days happens to be a "year" to those on the surface does not follow from items that recharge once per day. Or items that recharge once a month. Unless there's a natural cycle that's easily observable by the subetrranean culture, why shoudl they observe it as important, such that they'd count it?
That, of course, is also if their items recharge at surface dawn, which they may not. "Dawn" is the time the sun rises over the horizon on the surface - these people aren't on the surface, there is no horizon, and the sun never rises for them. It doesn't make logical (or metaphysical) sense to tie magic to rhythms that the people do not experience.