Accurate soft proofing of CMYK

I'm sending off files to a digital printer.  They've been requested as PDF or TIFF in CMYK with Fogra39 as the print profile.

I've sent off PDF test prints and received them back.  The CMYK Fogra39 profile was embedded.

To 'be on the same page' as the printer, I have exported the files from the PDFs that I sent as TIFFs.  Then visually checked the returned sample paper prints against these TIFFs on my PC screen (Windows Photo Viewer).  They look almost exactly the same.

Then I also exported TIFFs (with CMYK Fogra39 embedded) from my original CorelDraw X4 files.  I checked those TIFFs against the other TIFFs and the sample prints.  Practically the same.

My question is - When viewing my work in CMYK with Separations Printer set to Fogra39, there is only a small darkening/changing from the sRGB colours (my screens are X-Rite calibrated to sRGB).  However, going by the returned sample prints from the printer, and the exports to TIFF as viewed by Windows Photo Viewer, I would imagine CorelDraw X4's color management soft proofing should be as accurate as Windows Photo Viewer.  But it's not.  In fact, Windows Photo Viewer seems much more accurate (going by the sample paper prints).

The CMYK PDFs also look the same as CorelDraw X4.  But the TIFFs are actually the most accurate for checking against.

Can anyone throw some light on the above?