The bluish color of all color papers is due to a dye in ALL of the layers. It is there to adjust speed and to improve sharpness. This dye gradually builds up in the color developer (if you reuse it) and the developer becomes darker and darker blue. Of course, if you follow the published guidelines, you will know if you are putting too much paper through the developer.
In any case, the blue dye is never retained in the coating, nor can it dye the coating blue. Something else causes that blue color. I mentioned red safelight fog. It can also be caused by contamination of the developer with blix, and by omission of the stop bath after the color developer.
If you have leftover dye in the coating (blue dye that should wash out), then a simple re--wash should remove it, but I suspect that you have some other problem. I mentioned several above here.
The overcoat, as I tried to explain in my OP is just plain gelatin! If it is matte paper, then it also contains a matting agent to make the paper have a rough surface. And the dye is uniformly distributed throughout the coating in both Kodak and Fuji papers.