How does Toxic set work in Raid : Shadow Legend?

I need to clarify there is a difference between multi-hit attack and an attack that hits multiple foes (AOE).

A multi hit attack (one that say hits a single opponent 3x) has a single chance to trigger an artifact set debuff.

In your example of Banshee, her attack that hits multiple foes one time (AOE) That means each foe has a chance to receive the debuff. a check is made on each opponent with % chance to occur, increased by your accuracy, decreased by your opponent's resistance.