"Gain X% Damage with Hits as Extra" with "Does not Hit, but Poisons enemies as though Hitting them"?

I think most of my confusion comes from the wording of "Does not Hit, but Poisons enemies as though Hitting them".

These phrases come from:

- Acolyte of Chayula Ascendancy
- Poisonburst Arrow / Gas Arrow

Would love to understand how this interaction works.