If the pink light still penetrates the mesh and colorizing the hair with a normal material, without the hair shader plugged in, then it's likely to assume that the hair shader is the problem.
As I mentioned, the shader wasn't constructed for this purpose, it was for c4d's renderer and using polygonal hair.
There are a lot of things that don't work well.
As for the illumination tab, things like translucency, reflection, even shading affects the colors. It might be that the light hits the roots of the hair somehow and those transmit the color all over the hair, together with the bounces, it might be even worse.
To be clear: I meant that you might find the solution in the hair materials illum. tab, not the shaders. (pic1)
You can decrease the colorization, not completely but to a certain level. A Rayswitch material could also help. It won't be perfect with the hair shader and I'd make use of some multipass channels to get rid of those.
2.pic: RS render with the c4d hair material connected to the RS hair.
If you want more RS examples, you'll have to wait until next week when I visit my gpu-buddy again.