I'm not sure that the descriptions in the program correctly describe the corner phases actually, the phase in question isnt really braking while turning it, it's coming off the brakes while turning in.
So effectively the car is rolling outwards, and pitching backwards. If you consider this motion diagramatically, you can see that the only rear damper that is significantly active is the outside rear compression damping.
Basically, under full braking, both rear dampers will be maximally extended, and under full cornering the outside rear will be fully compressed and the inside rear will again be fully extended. So you can see that if you perform that transition smoothly around the outside of the traction circle, your inside rear basically stays where it is, and your inside rear goes full extension to full compression. Likewise you can also see that the outside front basically stays compressed and the inside front travels the full distance in rebound.
Hence for this transition, the rear compression damping and front rebound have the dominant effect on their respective ends of the car.