iCloud transfers message/mail contact history to other devices (unwanted)?

As part of troubleshooting some Family Sharing issues this past weekend, I logged my son out of iCloud on his new iPad and logged myself in. I then did the opposite - logged myself off and logged him back in.

What I noticed after doing that is that my contacts show up as auto-completes in the To: field of his email and messages apps. They're not in his contact list, but they do appear when he starts typing the name of the person to whom he wants to send the message.

I've erased all data and restored the device as new, but they keep coming back. This "history" now appears attached to his iCloud account.

I had to do some additional troubleshooting and also logged in to iCloud on my wife's phone before I realized what had happened, and she now has the same effect.

Unfortunately, this is not acceptable. I can't afford to have my son accidentally emailing or texting one of my critical work contacts.

I do not have iCloud set to back up any of my mail, contacts, reminders, etc