What happens when you "raise" the exposure is that you steepen the curve. This raises contrast but also significantly increases saturation - in all colour channels. Just look what has happenned to your foliage.
Yes, well put. All the saturations increase with underexposure. However, my point relates to the proportional red saturation. If we consider the total color value at optimal exposure, red is a certain percentage of that. If we underexpose red becomes a larger proportion of the total. At least it does on my IQ180. Try it on yours. Just add up the RGB values and calculate a proportion for each primary.
Simple exposure correction algorithms do not model this effect so the corrected image keeps the inaccurate red cast. Perhaps this is normal and we are expected to establish our own camera profiles for different lighting conditions? That's fine if the effect is subtle. A few profiles will cover most conditions. If the effect is substantial, however, modeling becomes a more effective way of handling it and that is up to Phase.