Yes, that is what would happen if you are sharing an Apple ID. If you restore them, they will show up on her phone again. She will also get your text messages.
When you purchase a new device for a family member, you need to also set up an Apple ID for that person. If your daughter is under the age of 13, then you would have to set up Family Sharing and set up a child's account. I've attached two articles so you can select which one you need to follow to set up an Apple ID for your daughter:
Over 13: Create an Apple ID - Apple Support
Under 13: Family Sharing and Apple ID for your child - Apple Support
As for recovering deleted Contacts, you can go to iCloud.com on any computer and sign in with your Apple/iCloud ID. Then go to the Settings icon, and once in Settings, scroll down to the bottom of the screen to the "Advanced" section. Click on the Restore Contacts option to see if you have a backup for Contacts from before she deleted them from your account. If you have a backup, you can restore it and iCloud will sync the restored contacts back to your device.
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