FOGRA 39 adding other colours to solid blocks of 100% colour

Also, because you are including the destination profile, the Simulation Profile or CM settings you choose in AcrobatPro will affect the separation numbers—I'm assuming you are checking the output numbers in Acrobat. Make sure Coated FOGRA39 is set as the Simulation profile.

Here's 100% Fogra39 cyan with US Web Coated SWOP set as the Simulation profile

With the Fogra39 the numbers are unchanged:

One of our companies uses 100% Magenta in solid blocks, and although it's correct in the artwork, when output to PDF using this profile, there is other colours being added to the solid blocks of colour, like cyan.

That could happen if your document's assigned CMYK profile is not also Coated FOGRA39. Check Edit>Assigned Profiles... and make sure the assignment is correct. Note that Color Settings doesn't necessarily show the document's profile Working CMYK and Document CMYK can be different—you want Document CMYK.

Your destination should have the Document CMYK prefix like this:

Thank you for the screen shots. They only show half of the story though. Please show:

- your colour settings in InDesign

- a screen shot showing how you see that the resulting colour has changed

- the exact version number of all software involved.