I think it depends on the store. The only one I have linked currently only takes a day at most usually. Sometimes a couple of days, but usually overnight. Some companies may take longer to process that through their corporate offices. Think it is supposed to be 48 hours, but maybe if it's your first time doing that linked, it might take longer I suppose?
Only thing you have to make sure of is that you did use your loyalty card when you checked out. I missed one once when I was in too much of a hurry and didn't type my phone number in on the self-checkout. Ha!
Sometimes it takes several days for Walmart Grocery to process. As long as your Account shows that it is linked, you don’t need to do anything. My purchase never shows as pending. I make a list of offers and bonuses I am expecting. If there are any mistakes, then you can submit a ticket.