I'm not sure if the bumpers are the same between the CS and Comp, but they certainly look like it. The obvious difference with the Euro bumper is that it doesn't have the cutouts for the side markers.
I've mounted 2 CS-style splitters on my M2C. I had to replace the first one along with the bumper because we hit some road debris.
In both cases, I used the mounting brackets and had to cut the bumper(s) for it all to fit properly. Unfortunately, I didn't take photos but I used the drawings from this site to figure out where to cut:
https://www.bmwpartspros.com/oem-par...JjaCBSZXN1bHRz
I measured from, as a reference point, the closest hole (for one of the screws) on the outside of the triangular cutout. I just sketched it out on the inside of the bumper and checked it several times before making the cut, taking care to stay away from the very front of the bumper. From experience, I can definitely say you have to make the cut that large for the bracket to fit properly. Also, discard the bottom front lower trim support (it's the long, felt-covered piece that is below the radiator). The splitter and brackets won't fit correctly if you try to keep it in.
I also used 3M double sided tape on the edge of the splitter. I really can't tell if it's used on the CS, but I wanted the extra adhesion and it fills the gap nicely so dirt doesn't get between the bumper and splitter.