Yes. If the bank successfully issue a charge back, meaning the merchant does not contest (happens when the merchant is at fault), the credit turns into permanent credit without you do anything. This can come really quickly.

Else, the banks would need you to complete and sign an affidavit before a permanent credit is issued. At least that was the practice a year or two ago.

I one time had a gymnastic training center operator in California charged my Chase card for several gym classes because they took payments over the phone and the card number was transposed. The credit came the next day after it was reported. On another occasion, another Chase card only being used once outside home (brand new to fulfill the 1st purchase for the bonus) and the info was skimmed. Later it was used at a 24-7 health club in California. When I called I found out it was a POS, meaning a physical (phony) card was used. On that incident, I had to do the affidavit. Before the affidavit form even arrived from Chase by mail, another charge from the same 24/7 club showed up, this time on the replacement card. Chase could not stop it because the initial authorization was done on "recurring expenses" category. Chase told me to add the new fraudulent charge on the affidavit and guess what, told me to track down the billing company to tell them it was a phony card in their accounting records! If I want to keep the card open, the "recurring charge" could only be stopped by the billing company!!! I finally tracked down the club's billing is done in an offshore location in Panama City, Panama, Central America! The accounting staff there told me it was a POS transaction but he made a note that this was reported a stolen card and NOT to be allowed again. Two months passed, no more fraudulent charge showed up. I canceled the card after the account bonus posted.