PDF in a tile or section may get immediately downloaded upon render in a live or preview site, and even while in the site editor!
This has to do with the file sending an unusual header that fails the system from detecting it as a PDF. Our initial investigations tell us that the affected PDFs were converted from other file types, like from MS PowerPoint or MS Word, and that the conversion process to PDF was also made through the same document processing applications where the originating files were created with.
The other option is to use third-party applications, like Adobe Acrobat Pro, to convert the PDF into a reduced version. We are also successful when we with Mac's Preview for conversion, using its Quartz Filter set to PDFX-3 Generic Document.
The behavior described may be also observed with interactive PDF, although the other options above might not apply as it disables the layer so the users can interact with the PDF.