I'm a pretty inexperienced helicopter pilot, but I'll have a go as a Physicist and say the reasons are all about the new 'direction of travel' air passing across the disc and therefore incorrect positioning of cyclic to counteract the flapback. You're initially in equilibrium with cyclic in the correct position to counteract all flapback. Applying pedal in either direction causes that counteraction of flapback to now be in the wrong direction because you'd need it to be more in the direction of the slip. This now means you haven't got enough roll input in the direction of the 'out of balance condition' airflow, so you flapback from that new direction which gives roll in the same direction as the pedal input. Similarly, you've also still got too much forward pitch counteracting flapback that is now no longer coming from quite the same direction as it was in the balanced condition, so the nose of the aircraft pitches down. This will happen with either pedal input and indeed with either direction rotor travel.