Does AppleCare warranty follow the device or the user?
The previous owner has to transfer it to the new owner.  See, "Is the AppleCare Protection Plan or AppleCare+ transferable?" under AppleCare Products Frequently Asked Questions, it states:


  Is the AppleCare Protection Plan or AppleCare+ transferable?
  
  Yes. If you choose to sell or give away your Apple product, you can
  also transfer the ownership of the AppleCare Protection Plan or
  AppleCare+. Please see the Terms and Conditions for complete details.