Hi gmjm,
Thanks for posting in Apple Support Communities. It sounds like this may be related to iCloud Keychain. This feature auto-fills your information like Safari passwords, usernames, etc.
If related to iCloud Keychain, you may see the option to "Approve Later" which you can choose if you'd like. Take a look at Set up iCloud Keychain - Apple Support for further details.
You may not need to sign out. But if you are prompted to sign out, you can do that from the iPad by going to Settings > [Your name] > Sign Out and on your Mac, go to the Apple () menu > System Preferences > Apple ID > Sign Out.
Take care.