Something is fairly inconsistent in what you describe.
If you embed fonts in a PDF file, those are the exact fonts used for displaying and printing from that PDF file, regardless of any fonts installed on your computer or in your printer. Acrobat (and Reader) also give preference to embedded fonts over anything else.
You are claiming though that when you “view which fonts are embedded only the .ttf are showing up.” Well, that means that whoever is creating the PDF file is not embedding the .otf (OpenType CFF) fonts.
What I most strongly suspect is that your “one user” is actually creating the PDF using Microsoft's built-in “Save as PDF” as opposed to Acrobat's “Save as Adobe PDF” as provided by the PDFMaker plug-in provided by Adobe Acrobat. Microsoft Office has a terrible, known bug whereby it never embeds any .otf fonts in any of the PDF files it creates, but rather either puts in a raster bitmap or a reference to a non-existent font. Adobe has alerted Microsoft to the problem numerous times, but Microsoft apparently has its own priorities …
The fix is to make the PDF files using Acrobat's PDFMaker “Save as Adobe PDF” from Word!
- Dov