No. You used to need to wait for the next autoattack. Many "on next hit" abilities were like that, and they've all been changed to be resets but still, it was a significant buff for Nasus in particular since Q is his primary source of damage.
Also the scaling is 3 damage normally, it gets 6 from big monsters/cannon minions.
Yeah, getting 6 per kill from large mobs was one of the more recent changes and probably what made him strong(er) in the jungle (he wasn't a terrible jungle before, and the jungle has only been made easier).
Bear with me... things are about to get grizzly! Fox is HOT!