Phil from the Shopify Support team here. That's a great question!
When you issue a refund on Shopify's end within the admin, we send the refund immediately, but the customers bank will take some time to actually process it. This is entirely dependant on their bank. For example, have you ever gone and requested a refund before on your credit card, usually there is a several day waiting period before the money appears back onto you statement. It's usually around 3-5 days. Similar to paying off your own credit card balance. Your customer can find out exactly how long a refund should take to show up in their bank account by contacting their bank and you can safely tell your customer that the refund has been sent.
Hope that helps!