SureAI

So, I'm replaying Nehrim and a little problem occured in this quest.
I have two versions: play 1, and play 2.

I'm at that part where I have to go to the Temple and defeat Templar Janus.

Play 1: Kim ran with me to the Temple, everything was all right.

Play 2: I'm running alone, Kim is nowhere to be found, I see him running towards me only after 2-3 minutes.
The quest is completable in this way too, so he talks to me after that.

What I'd like to know is that is this some kind of bug, or did I do something wrong? (Though I did everything according to the instructions)

What part of the quest are you at? It's somewhat difficult to infer this from your post.

Ah, sorry!
The quest is the Impotence of the Almighty. (I was very sleepy yesterday.)

So once again...

Together with Kim I defeated Jagal, and have to get to the Temple to kill Templar Janus. (Ostian)

Is Kim supposed to come with me , or do I have to wait for him at the Temple? (Because for the first time I played, he followed me. For the second time, he was just standing in the Storage Cave and came after me after 2-3 minutes.)

And sorry... Exams made me very tired... :S

Kim is supposed to come with you. Unfortunately, thanks to Oblivion's wonderful AI engine, she doesn't always. But I never had a case where she didn't ultimately follow up (normally when one arrives at the central place of Ostian).