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).