Your Apple ID was used to sign in to iCloud using a web browser

It is a matter of accounts. You only get that message if you are the account owner. To me it is sounding like multiple people are sharing an account and somebody signing in elsewhere is triggering that message (that is normal behavior).

Your solution is really to set up different accounts for each person since that is how it is designed to be done. You are working against Apple's basic account functions and security protection. At worst only you should normally see that message.

I don't know if you could prevent this from happening if you made sure cookies were enabled from Apple and not deleted in the browser. Some browsers automatically delete them.

This article explains how to create a new Apple ID (create an Apple Account) --> How to create a new Apple ID - Apple Support

Are you all using the same Apple Account? Only the owner of an account should receive that kind of email.

If you are all using a single account then you should really each be using your own account.