When you have a TIFF or PNG as a background image, schedule, detail or combination of the three and you need to create a PDF of the sheet, you MUST use the PDF driver from the Plot dialog box rather than the button on the Output ribbon. There are a few MAJOR differences between the two. When you use the icon on the ribbon (and have the option to prompt for a file name turned on) you will see this dialog box which has fewer options. Fewer options means less control over how the PDF is created and ultimately how it looks.
But when you use the Bluebeam PDF driver from the Plot dialog box you have more options to pick from, most notably the Application drop-down where you can specify AutoCAD Drawing with Photographs.
If you have a mix of drawings that are linework and some that are a combination of linework and images, this may require you to create PDFs separately (ones with linework and ones with linework/images) but you can quickly combine and rearrange PDFs using Bluebeam Revu.
So, if you notice that your TIFF or PNG background image isn’t plotting correctly, then you may need to change the way you’re creating the PDF.