I have spent a lot of time on this thread and after reading all the posts I have figured out the issue.
I share my Apple ID with 2 ipad mini's, 2 Ipads and 2 Iphone 5's, and it was driving me crazy. I could not figure out why all of my devices were showing my picture on all 6 devices. I also, did not want to give up sharing contacts with my wife, nor an Apple ID for App purchases. Come to find out, we can absolutely have both worlds while resolving the airdrop situation at the same time.
If you want it to be resolved, each person must have their own Icloud. They must not be sharing the same icloud ID as you are. I had to create an "Apple/Icloud ID" for each of my family members and sign them in via ICloud.
1. Go to ICloud.
2. Turn off each option (Contacts, Calendars, etc.)
3. When asked if to keep on iphone or delete choose wisely. If you want the same contacts to sync with the new icloud account then keep the information on the phone. If you don't care, then say delete.
4. Go to the bottom of the icloud option in settings and click delete account
5. Once Signed out, creat a new ID for that family member.
Once this is done you must sign the device out of your Apple ID in Facetime and IMessages. This will delete any connection the phone has with your Apple ID. Then sign back in via the new ICloud ID.
Lastly, go to Mail, contacts and calendars to my Info, and tell the device whose contact you want to connect it to
Now I know you are thinking "But I don't want them to be signed out of my App Store downloads" cause that was my concern. This is a separate option in the Itunes & App Store menu and will not effect this.
Once this is done make sure you update your contacts with the new device information in all devices so the pictures will appear. Otherwise it will recognize the device, but will not connect it to the picture in your contacts.
Now...if you still want to sync contacts, go back into "Mail, Contact and Calendars" and add the the icloud device you want to sync with and click "Sync Contacts".
After this you should be all set.