How to stop 2 iPhones on same account syncing

Immediately stop sharing an Apple ID. “Both our iPhones (on the same account)” is just fine as long as the account being referenced is a cellular carrier account.

Make sure that each family member has a unique Apple ID - Apple Support

The person acquiring the new Apple ID must first thoroughly cleanse her/his device(s) before “moving in” using the new ID.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Stop sharing an Apple ID with someone else; Apple IDs are highly personal and should never be shared between different people→How to “unshare” an Apple ID - Apple Community

Each person should have their own Apple ID. This has been the recommended approach for a very long time. Having 2 devices using the same Apple ID are meant to sync seamlessly so a user can start a task on one device and continue it on another.

Make sure that each family member has a unique Apple ID - Apple Support