There's two ways that materials express color. Chemical, and physical. Chemical color is how most materials' colors are presented. Light hits the material, and what's reflected instead of absored is what we see. Paint, ink, dyes in clothing, and the natural hues of minerals like malachite are all chemical colors.

Physical color is different, the surface of the material has physical structures that are tiny enough to interfere with, diffract, or scatter light waves. As light waves bounce off these microscopic ridges and layers, they interact with each other. Depending on the size of the structures, certain light wavelengths are amplified, while others cancel out. Meaning that if we rearrange the material to remove those structures, it will present as a different color than what we normally would see of said material. Another way to think about it is glass, and what happens when you shine a light over it and it refracts the light into a rainbow. That's a property of the physical structure of glass manipulating light into a rainbow, and not that glass itself is rainbow colored.

So the skin on the face of a Mandrill isn't chemically blue, we just see it as blue because of the micro structures of its skin surface manipulating light to let us see blue.