If someone poisons a mystic, does that activate mystic ability? Does the poison-er take a clix of mystic damage?

Was the question not clear?

Poison doesn't trigger Mystics/CrossGen/Arachnos. From the PAC:

POISON (optional): Once at the beginning of your turn, as a free action, this character may deal 1 damage to each opposing character adjacent to this character.

MYSTICS When this character takes damage from an attack, the attacker takes 1 damage. This damage is not an attack and cannot be reduced.