My account has been credited with a refund with Apple Billing & Payments, but I haven't received the money yet. What should I do?

Apple Billing and Refunds had taken a payment of USD 49.99 from my account. But since it was not the transaction I expected, I requested a refund. I also deactivated my payment method and my debit card. I received an email saying that I had been refunded as requested, but the amount has not been added to my account yet. What is the reason for this? What should I do next?

Since this was cleared through a POS/ATM transaction, will I get the same money after I reactivate the card? Do I need to reset the payment method?