Why she chases you instead of killing you on sight
Instant deaths are cheap scares. We wanted being found to be the start of something worse.
In early builds, if Madam Koi Koi saw you, it was over. That's a jumpscare, but it isn't much of a game: you learn nothing, you just reload.
Now being seen is the start of a chase. She comes for you, and you have a few seconds to break her line of sight, put a door between you, and get into a hiding place before she rounds the corner.
Places to hide, and how she finds you
You can hide in lockers and wardrobes, under bunks and beneath desks. She knows that too. She stops at hiding places and checks them, one at a time. If you leave your flashlight on inside, she sees the glow.
Evidence and keys
The same update made the keys turn up in different places each time you play, and made all the evidence necessary before the gate will open. You can't just sprint for the exit: you have to learn the school, and the story with it.