How does Zac's passive trigger on-kill effects?

No, "Zacies" are worth the same as pets (Elise's spiders, Malzahar's voidlings, etc.) They WILL give you a bonus if killed by Cho's R, Nasus's Q, etc, but it will NOT count as a champ kill. I was wondering the same thing and tested it out with some friends in a custom. Then again that was 4 days following his release.

EDIT: As to clarify the answer, just like for Kog'Maw and Yorick, the killing blow against Zac is the last hit that turns him into the 4 "Zacies", not the last hit against the last "Zacie". This is the only hit that counts as a champion kill against him.

EDIT 2 : I'm getting out of the boundaries of this question to adress some of your doubts. In LoL, a kill has several definitions. First of all, the one that counts in the kill score, for killstreaks, etc. : It is the one that turns the player's screen black-and-white, to be as precise as possible. In the case of all passives that give you "a last chance", such as Anivia's and Zac's, it is last hit that "forbids" the player to come back (killing the egg, the last "Zacie"..). Then again, as to the last hits that trigger abilities, it is another definition that usually comes into play. It's the "entity" last hit. Every "living" structure in LoL has an entity type. For, creeps it's "creep", for champions it's "champion" (and this counts as the "champion-kill" for abilities), for pets it's "pet-controllable" or "pet-IA" (names may not be exact), and this is the case for Yorick's ghost, Elise's spiders, Malzahar's voidlings, etc. AND Zac's "Zacies". Using an ability that scales on kills checks the entity type. And in the case of Zac, retrieves a "champion" type. It then awards the player the champion kill bonus. Hope this clarified everything for you.