Are macOS Spotlight privacy settings shared between parallel installs?

I have two independent copies of macOS Catalina installed on two different disk partitions.

Somehow, when I change Spotlight privacy settings in one of them, same settings and up applying into another system after I boot it up.

How is that possible and how can I fix it?

Adding a volume to Spotlight’s Privacy tab adds a ‘no index’ file to the root of the volume. This file will then exist for the other OS to read and be applied.

It’s not possible for one OS to index a volume and another not since the index is stored in a hidden Spotlight folder in the root of the volume, not unique to an OS.