Hi there @MicAnizeMi!
Don here from Shopify.
If you are working with a third-party print-on-demand company that is printing your designs to be shipped out to your customers, they would be the ones you need to contact with any questions about their process.
You can click on 'Get support' next to the name of any third-party app in the Apps menu in your Shopify admin to get in touch with their support team, or you can also find those contact details on the app store page for this specific app in the case of Printful.
They would be able to provide support for their app and service and should be able to answer any questions you have about their processes.
From my experience, it would likely not be possible to have a fundamental aspect of the process such as payment changed in this way, but the support team for the printing service you use will be able to confirm for you fully.
Let me know if there's anything else we can help out with from here in Shopify.