Elemental Incarnation: Fire and damage negation

When an effect occurs when you take damage, like Base Form EI: Fire, and you take a hit but negate the damage with an armor slot or a feature, the retribution damage still happens?

Likewise, when a monster causes the poison condition upon causing damage, if a PC is hit but reduces the damage to 0, the PC is still poisoned?

"Elemental Incarnation: Mark a Stress to Channel one of the following elements until you take Severe damage or until your next rest:

Fire: When an adversary within Melee range deals damage to you, they take 1d10 magic damage."