Family sharing displaying my contacts

I just set up family sharing for my children on their mini's. I created their own accounts under family sharing and my contacts do not show up in their "Contacts". However, when they go to compose a new text all my contacts show up. I don't have anything in their that i don't want them to see, but I don't want them to accidentally send an iMessage to people they don't know. I have checked the settings and nothing is set to sync on their devices.