Relevant Product: Exclaimer Cloud - Signatures for Office 365
Why am I prompted to sign in and authenticate for any additional Microsoft 365 accounts that have been added to Outlook?
If you weren’t expecting to be prompted for an account and it doesn't appear in Outlook, chances are that the account exists in another Outlook profile for the logged-in user.
You can check for additional profiles by going through the Mail options in the Control Panel.
The Cloud Signature Update Agent will check to see if there are any signatures for the additional mailboxes.