Azir's minion interaction causing possible item baiting

Hey, so I was wondering this a while ago and couldn't really find any clarification on it, so I wanted to ask. Since Azir's minions don't proc on-hit effects (i.e. red buff) and only procs spell effects, then isn't Nashor's Tooth just a bait for a bad item on Azir? Nashor's Tooth's passive procs on-hit, so does that mean Azir's minions don't proc Nashor's Tooth? I'd appreciate a clarification on this since it seems like that interaction really negates the point of recommending Nashor's Tooth on him.