I have an issue, I have cancelled a couple orders and refunded the money to a little few of my customers.
Although it's been over 10 business days and I keep getting messages from those customers saying they still cannot see the credit on their bank statement yet.
Is there anything that I have to set up on my store? Why haven't they received the funds yet? Is there anything wrong?
Refunds as you know can take up to 10 business days to reflect back on a customer's account as per their bank's processing times; however, depending on whether or not the refund took place within 24 hours of the charge could be the culprit. If you provide a refund within 24 hours of the original charge, then the bank would see this as a "reversal of funds" which means the funds were refunded, but they typically won't reflect on banking apps. If this were the case, then your customers would simply need to call their credit card companies to confirm the refund took place.
Another thing to be mindful of is the payment processor used at the time of the transaction. For example, if they paid via Paypal, those funds will be deposited into their Paypal account, or processed back to their card associated with their Paypal account which could lead to a delay in seeing the funds. When you open the order(s) you've refunded, and scroll to the order timeline, what payment provider appears? Do the refunds show successful, or failed?
If you're using a third-party payment provider, and the refunds appear successful in the admin, then you'll want to check your account with the third-party payment provider to ensure the refunds were processed on their side. If they haven't been processed, or if the refunds are taking a longer than expected time, then contacting the payment provider directly will be your best bet as they can investigate further.
If these orders were processed with Shopify Payments then let me know as I can have our teams investigate the refunds.