This seems to be a 'Can we see the trees for the forest?' type question.
There are three distinctly different things happening in human vision. One is to differentiate the colors, and the second is to resolve the details of the shape and form. Then, there is the original vision systems, such as that still used by the fly, that senses neither color nor detail, but just motion. Basically, all it resolves is a moving shadow across the vision sensors. If there is no movement, there is no 'vision'.
In humans, our monochrome vision can resolve high detail, as in seeing the trees. Our color vision resolves the overall background color, as in the forest. It seems our eyes map the the overall color detail on top of the detailed monochrome image to create, in our mind, the final 'color' high-res picture. That is, we do not stop using our monochrome sensors just because the light is bright enough to resolve colors. Our color vision adds to the monochrome vision.
I could imagine the eye of this hypothetical being would have to be very similar. That is, monochrome non-differentiated spectrum sensors to determine detail and movement, and the more general spectral image processors to define the color. In terms of pure survivability, the faster monochrome detail and motion response would be a first-alert system, and the slower (I suspect) spectral image processor would provide more information after a very brief lag.
In our first televisions and other image capture media, we generally either used black-and-white images, or color images, and did not combine the two. That is, the original CRT screens were either monochrome or color phosphor screens, but not both. After all, the same color signal activates both the monochrome and color sensors in our eyes. I suspect the televisions of this society might have developed a different dual-process form of television - one that produced very fine monochrome detail imaging, and a second system that mapped color onto this monochrome image. Maybe filters that went over the screen, cycling through the color spectrum, in synch with the monochrome image. That way, the monochrome projects the detailed trees, the color filter device fills in the forest color.