You were referred to their website through a Social Media post where the poster was paid for the referral or sometimes through website advertisement. On their page they offer a "reading" that is actually a free trial to a subscription that you will be billed for if you do not cancel.
As with any fraudulent charge you have to contact the merchant and if unresolved dispute the charge through your credit card that is being billed. As you have found out, all PNO's (Visa, MasterCard, American Express, etc) use Automatic Billing Updaters that transfers any recurring charges from merchants to your new card. You have to actually block those charges through the bank of the issued card to prevent that from happening.
This has nothing to do with Apple and you would see that charge whether you had downloaded their app or not.