Cass will passively generate stacks on her passive over time (10 per minute) and gains stacks simply by enemy champions being poisoned (i.e. from her abilities, but also gets stacks from Teemo's Toxic Shot, Singed's Poison Trail, Twitch's Deadly Venom, Gromp's Toadstool Armor... I think that covers them all) whenever they take poison damage, so each tick of poison counts.
That is, unless you're talking about the stacking debuff applied by Twin Fang, in which case, using Twin Fang will cause the debuff, and debuffs from this ability can stack and increase poison damage for both of them, rather than just refreshing the duration on the debuff like you see when you take multiple autoattacks from Teemo, for instance.