Are skills supported by Cast When Damage Taken supposed to have a mana cost?

There is a difference between a skill not having a mana cost and you not having to pay that cost.
Skills have a mana cost. To cast them manually you pay this cost. Trigger gems cast the spells for you, bypassing the need for you to pay the cost which the skill still has.

This doesn't matter much at the moment, but if some future unqiue item, say, increased a skill's damage by a value based on it's mana cost, or any similar modifier, that would apply to triggered spells because they have a mana cost, you just avoid paying it.