In general, what will happen is that when someone makes a contribution through your ActBlue merch form, we will get an automatic notification from ActBlue. We will then make the merch that the donor has ordered, charge your card on file with us for the cost of the merch, and ship the merch to the donor. Note that you have received the donation into your ActBlue account before you are charged anything for the merchandise!
If it's the first time someone has ever ordered merch from your ActBlue account, we will send you an invoice prior to making and shipping the merch. When you get the invoice email, just add the information about the credit card you would like us to charge for future orders, and Square will securely store the card information for us so that everything in the future will be seamlessly automated.