the Daedric Trickery set says that it procs off damage done. Any damage done, "when you deal damage". No other conditions like range or melee, dot or direct, etc.

however it does not proc from damage done by the Elemental Susceptibility spell. Neither from the direct damage done from applying a status effect, nor from even the damage over time from the burning dot.

video showing it, here

any other kind of damage done works, but from this spell no. And this spell works with proc sets because with others like Serpent's Disdain it does work as it increases the durations of debuffs placed by this spell.

But it doesn't proc the Daedric Trickery set.