Hi Ranneburton,
As we understand it, you set up an Apple ID for your son but you're finding that when contacts are deleted from his phone, they're also deleting from yours. Is that correct?
If so, it sounds like it will be beneficial to double-check the Apple ID and iCloud settings on both devices, as this would generally happen if the same iCloud account is shared between the two. Try tapping Settings > [name] to make sure that you see a different Apple ID at the top on both devices.
As another possibility, do either of you use a third-party account like Google to sync contacts? If you do, check Settings > Contacts > Accounts and compare what you see there on both devices. If you happen to be signed into the same account, deleting a contact from one device would delete it from the other: Use other contact accounts on iPhone - Apple Support
Let us know what you find.
Regards.