If it helps...
The combination of inflow roll and flapback makes the disk move up or down at a point just left of the nose, but they have their greatest individual effects at different speeds. Those of inflow roll are greatest at low speeds, on leaving the hover, and decrease significantly with speed. At higher speeds, dissymmetry of lift will be the most dominant force.
As the effects of flapback are greatest at high speeds, the Tip Path Plane rises near the retreating blade when first moving from the hover, then moves round towards the front as speed increases.
As for having to push forward, one simple explanation is that, as you push the cyclic forward, the body lags behind, but, when it does catch up, it centralises the cyclic, assuming you haven't moved it. So you have to push forward to keep things going.
Phil