Preventing other users on same Mac from accessing my iCloud Drive

There are two users on the Mac, including myself, both administrators (Mac owned by both of us).

I have personal files stored on my iCloud Drive, thus I have set privilege of the sensitive folder under my iCloud drive to 'no access' by 'everyone' - it works initially, as when the other user logs into his, goes into my iCloud drive via 'users' on finder, and can't open that sensitive folder, with a prompt that says no permission. However next time when we go to my iCloud Drive from his Mac login again, the sensitive folder becomes accessible!? So I'd log into mine, change the folder back to 'no access', again it works at first, but at some point it would somehow change back to accessible to the other user, seemingly by itself.

Is there a way to ensure folders and files on my iCloud Drive aren't accessible by other users on the same Mac? Searched through the web, but it seems people only talk about "how to share" and not much on "how to prevent access by others".

I was also rather shocked when I first found out that my iCloud Drive was completely accessible from the other user on the Mac...so much for the security and privacy I thought I had.