I'm not a specialist as well, but I did some routines to read out and process the raw images in LabVIEW. If you just display the RGB values as is, you will get an image pretty bad colors for two reasons:
1) The raw images have no gamma correction built in
2) Without applying the color matrix an R pixel will also pick up some green and blue component, the same is true for G and B pixels. I think this is due to the fact the filters on the bayer pattern sensor have to be relatively broadband.
Using the color matrix I have been able to convert from the rawRGB values to sRGB used for display (after interpolation from bayer pattern to full resolution) using the following equation:
sRGB = ColorMatrix x rawRGB
with sRGB and rawRGB being a column vector of (R,G,B) respectively, and ColorMatrix being the 3x3 matrix as shown in the camera (defaults shown in image attached). Warning: after appling the ColorMatrix you might/will get pixels with R, G or B out of allowed ranges, so you have to clip them to 0/max. I'm not sure, but this might also be related to the limited color space using sRGB.
Afterwards I applied gamma curve and had to strip down R,G,B to 8 bit for display. Finally this has shown the image close to the camera's screen and MP4 playback, so it looks like I guessed well how to process.