Cap on the amount of remaining aps

... Two? They only have one.
Question is, whether the databases added that into HP and MP, OR into HP OR MP. Care to check out? You should notice if both your MP increase like hell, or your HP do. Or both, for that matter.

Judging by this, HP/MP don't have any AP at all. If you have less than the "max for your level", you can do reset from them into normal str/dex/luk/int. That's why the game doesn't know which it is.

When you overrun the "available AP" it just acts like they're spent in HP/MP without increasing either.