Order printer Pro is designed to automatically get your Shopify store domain in the link if your store complies with two important aspects:
The store has "Online store" sales channel (basically if you have a website)
The Online Store is not password protected.
If both of the above are true, then the app uses the custom domain when generating the PDF link automatically. Therefore, when a customer clicks on the link to download a document, the domain would start with your store domain name. E.g.
If the link generated directs you to your storefront instead of the PDF, this is because Shopify will block the links that use your domain if the password protection is still enabled. If the website is public, then the link provided by the app will work smoothly and use your store domain by default.