While EInk has patented a black particle in white fluid display, the shipping article is a dual particle system consisting of white particles of one charge and black particles of opposite charge.
These are electrophoretic displays - which is just a fancy way of saying "moving particles through a fluid with an electric field". The particles themselves come pre-charged and the applied voltages creates an electric field to drag the particle around in the display. The particles are prevented from sticking to each other through a process of steric stabilization. The particles are meant to keep their locations in the fluid through the control of viscosity in the fluid.
The particles and fluid are encapsulated in small transparent flexible spheres (they call the black and white spheres in fluid the "internal phase") which are applied in a uniform layer across a TFT panel. The micro-encapsulation is to prevent lateral migration of particles from lateral electric fields caused by neighbouring pixels being at different levels.
The grey scale is determined by the state of white vs. black particle mixture. Because they have opposite charge one can easily see that full voltage one way will pull all the black particle to the top whilst full voltage reversed will pull all the white particles to the top. An intermediate state is a mixture of the two.
Where the problem arises is that there are many possible voltage settings that could potentially produce the same gray-state. The reason is actually quite simple, if for example you have a grey state that is only slightly darker than the whitest white, that means that you only need a few dark particles near the top. Where the rest of the black particles are does not determine the darkness but they will effect the electrical charge state in the cell. You could have all the black particles at the back of the display or all in a layer just under a bunch of white particles.
What this really means is that there is hysteresis in the system and the appropriate voltage to apply to a pixel to get a certain grey-scale will depend very much on it's history. If you have two scenarios 1: you have 5 scenes in a row where you have a pixel being white and then need to drive to black on the 6th frame or 2: if you have 6 scenes in which the pixel is at the same black level. Those two scenarios require different voltages on the pixel when you transition from the 5th to the 6th frame.
The controller that drives these displays tracks the voltage history of each pixel over time, but eventually it runs out of room to be able to hit the right gray-scale in the next frame. What then happens is a display reset in which the pixels are flashed to white then black and then re-written. This starts the tracking of the optical trajectory all over again.
Typically the reset pulse happens every 5 - 8 screen refreshes.
So no, the applied voltage does not inject charge in the system, the charges are already present, they are moved around by the applied voltage. No, the reset pulse is not to correct the adjacent pixel corruption. That is solved by micro-encapulation. This is a two-particle system, not a system of black particles in White ink.
Here is a cross section from a patent USPTO 6987603 B2:
122 = spacer ball to maintain separation of front panel from TFT
104 = the flexible micro-encapsulation - in it's crushed down state in a display
110 = a white/black particle
108 = a black/white particle
118 = TFT electrode
114 = the common (aka Vcom) ITO electrode