Those dark bands occur when you use a POLARIZER with a wide angle lens. The amount of light blocked by a polarizer depends on the angle from which the light source originates. Since a WIDE angle lens is collecting light from a broad range of source angles, SOME of those source angles will have a stronger polarizing effect than others. Polarizers work best when the true angle of view is limited (which means you're using "normal" through "telephoto" focal lengths... but avoiding "wide" angle focal lengths.)
The ND filter in your sample shots is undoubtedly (as everyone else has already pointed out) really a polarizer. You can stack two polarizers to create the effect of a tunable variable neutral density filter... but that's not the same as a true neutral density filter (one that has a fixed density and cannot be "tuned" or adjusted.)
A true ND filter is simply decent optical grade glass which is evenly tinted to block light light equally at all wavelengths regardless of the polarity of the light. In other words, had you used a simply ND filter rather than a variable ND, then the light would have been blocked evenly and all would be well.