It is unfortunate, but Acrobat does not provide information about the page rotation in the UI. The only way to know the page rotation is to run this script in the console window.
this.getPageRotation(nPageNum);
If you create a stamp from a PDF that has a rotated page, then it is placed rotated. Many applications create rotated pages when a page is originally in landscape orientation, but not always. Which is why the fix is to rotate the page in the stamp file.
You can read about page coordinate spaces here.:
https://www.pdfscripting.com/public/PDF-Page-Coordinates.cfm
I finally figured it out. I had to go back to the original drawing I created in AutoCad and rotate the stamp there. Once I created the PDF in that configuration, the stamp looked right side up. I have been fighting this for years.