That is a very screwy workflow. Why open a PDF in Photoshop, effectively destroying much of the information while rasterizing text, and then save it as a PDF in Photoshop?
Tell them to create the PDF as PDF/X-4 from InDesign and send you that.
PMS values in InDesign are actually stored as LAB values, not CMYK. If creating PDF from InDesign and forcing spots to process and all process to CMYK, then what CMYK values you get depend upon the color space designated for the output PDF. Then, you have a similar issue rasterizing the PDF file in Photoshop. CMYK values may change depending upon the color spaces involved.
In either case, as Bob indicated, this is a strongly non-recommended workflow. Quite frankly, you are performing extra steps which I guarantee degrade quality and are a source for multiple, probably unexpected color conversions CMYK=>C'M'Y'K'. Ugghh!
And yes, we most strongly recommend PDF/X-4 without any color conversions exported directly from InDesign.
And finally, use of spot colors for print workflows where there is no intention of using extra colorants is simply looking for trouble. You can use Pantone color definitions, but at least use the Pantone Process definitions, not the spot colors!
What I suppose why they are opening in Photoshop is that they want to convert spot colors into process colors and don't know how to do it properly in InDesign.
You should inform your client on the correct workflow:
Create PDF with Export PDF/X-4. If no spot colors are wanted, they should use the Ink Manager, which is found either in the Swatch Panel Menu or in any Output Dialog as in Export PDF.
Tell your client, opening an InDesign or Illustrator PDF will rasterize vectors and text at the image's resolution which cause a loss of quality as it is much lower than the device's resolution, and it will probably result in colored 4c black instead of clean K-Black (or the same with grey), and it will loose different color spaces and convert them into the PSD file's color space. This workflow is a no-go.
To the LAB and CMYK values was said everything from Dov and Bob. The correct CMYK values are not found in any color book as they are different for different output color spaces. Without knowing the color space (= color mode with profile) it makes no sense to specify CMYK values.