Comment by miahi

They work exactly the same as a screen. Orange is not pure red, it is red + yellow, and yellow is red + green. So orange is red + _some_ green. The in-camera processing will render the image based on the sensor input and the known properties of the filter (think of it as a color profile, a mapping between what the sensors read and the color). And the processing includes color interpolation for each pixel, as each pixel (photosite) only has one color filter, but the resulting image pixel has all three colors; these are calculated based on the neighbor photosites.

Different sensors/cameras have different filters, and combined with the manufacturer specific post-processing this gives different cameras/manufacturers a different color rendition and feel.