Pretty creepy? Possibly, but already normal
This sounds like the Visa Account Updater service (and presumably the Mastercard equivalent) which in the case of you arranging a recurring payment with a merchant (e.g. for a magazine subscription), provides that merchant with your new card number and expiry dates when your old card is replaced because of expiry, loss or theft. See http://usa.visa.com/merchants/grow-your-business/processing-solutions/account-updater.jsp for details...