back up iPhones on iMac

I haven't used a machine backup on my iPhones for many years as I find iCloud much more convenient. However what I suggest you do is create two user logins on your Mac each with a different Apple ID then do the hard backups separately.

Login into the Account that is associated with the iPhone and then plug the iPhone into the iMac.

see > How to back up your iPhone, iPad, and iPod touch with your Mac - Apple Support

and > Back up iPhone - Apple Support