A curse is not a trigger-based mechanism — that is, it is not "do something and receive some punishment." In stories, those cursed for their own actions were typically cursed for violating a contract, rather than due to the inherent nature of Curses themselves.
Like Prophecy, curses are not unbreakable. The stronger the caster's magic, or the higher the proficiency in Execrantia or Hex, the more likely the curse is to become reality.
A curse is a broad concept — it can refer to a form of Mana , or it can be a tragedy bound by the chains of fate. Relatively speaking, Hillkind have a stronger ability to control magic, because the curse flowing in their blood is itself a form of mana. The vast majority of curses are magical, though individual counterexamples include Daemon R. Brigid's Execrantia (which directly manipulates fate itself).