Our PDF Stamper renders the stamp in the upper-left corner of a transparent A4-sized rectangle, then layers that rectangle on top of each page of your original PDF and scales the rectangle up or down to fit the native height of each page, flattens those layers together into a single composite, and makes a new PDF of the result.
You can test the result by using "Send free download link" to send yourself a link, once you've set up PDF Stamping for your product and at least 15 minutes after you've uploaded the PDF file for that product.