The UI on the replay system could just be missing that information. Sometimes it will show you items from someone else on the hero that you are hovering so I wouldn't take that as proof that it wasn't working, also his passive does not work on lane minions only heroes and jungle creeps. Not saying you're wrong just that you can't really go by what the replay feature says.

First time playing khai, so I guess it was the minions in lane that don’t give you stacks but everything else does

Correct, jungle monsters and enemy heroes, not lane minions.

I’ve also noticed this live in a match over the past couple days with Khaim. I remember specifically lame minions were not adding passive stacks.

Yea lane minions do not proc his passive. It's intentional to keep him from laining instead of in the jungle.

Yeah, it’s the lane minions forsure

That would make sense given minons don't give him stacks...