How does it work? Do they hand paint the screen? How does it actually add red or blue to an arbitrary shade of gray which lacks any chroma? Does it work with video too?
Imagine that each grain is blocking a 'pixel' of the negative. For simplicity of this explanation, I'll pretend the grains are red, green, and blue. If there's a blue grain, only blue light can get through, and thus the luminance is baked in specific to the amount of blue in that region. The same is true for the red, and the green.
Thus, each 'pixel' of the negative isn't determining a monochromatic luminosity (ie black and white), but instead telling the luminosity of a single channel of red, green, or blue.
When the grain filter and the developed negative are combined, we get natural colour. The same filter is used for generation and display.
Another way to think of it is like this: Each pixel on our screen is actually 3 subpixels, each defining red, green, and blue, and we format our image to alternate between telling the red, green, and blue channels how bright to be. This is doing the same, but the subpixels are distributed randomly because that's much easier to make.
EDIT:
If you organise the grains in a geometric pattern, you get Dufaycolor[1].
I may be daft, and your explanation sounds reasonable but I still feel "magic + potato starch" :-D
The starch grains were randomly scattered on one side of the photographic plate, and acted as filters so that small portions of the plate would capture certain colors. The plate was then developed as a positive image.
When you would shine light through the developed plate it would go through the starch grains (still on the plate) as well as the developed image. The developed image controls the luminosity while the colored starch grains again act as a filter and control the hue of the transmitted light, roughly reproducing the original scene.
This part is key to understanding. The plate with the starch-based colored mosaic is not simply a filter used upon capture to be removed after (as most filters are today), but also a filter to be used upon viewing. Since the same exact “filter” is used for both capturing and viewing of a given photograph, it allows the mosaic to be random, simplifying creation of the filter.