Help Needed Please

These very lovely icons (by the incredible_loveunrequited)have some amazing coloring, I love the intensity of the saturation, the contrast, all that jazz - except I can't seem to replicate it. I've tried curves, selective color, saturation, and contrast and either get a really grainy image, an overly saturated image to the point where it almost looks posterized, or colors I didn't want at all. I've searched past tutorials and I can't seem to find one. I was wondering if anyone has any tips or ideas. I would really apperciate any feedback.