Thank you very much for your time and effort. I once had a trial Version of Photoshop CC installed and if I remember right, there was no color shift. Otherwise, I have Blender, 3DS Max, Gimp, Fusion, Lightworks.... and I never had problems with a color shift in any of those.
As soon as I can, I will test adding the sRGB....profile manually and look if there is something wrocg with the white balance setting as suggested by @Engine44. The thing is, I can't try anything until Monday because I don't have access to my PC at the weekend. If this does not work, I will contact the Customer Service.