Why it doesn't matter if tail produce lift or downforce for neutral point position?
The neutral point is the lengthwise location of the moment reference point where the pitching moment will not change with a change in angle of attack. It can be defined for a wing alone or for the whole airplane.
Of course will a change in the incidence of the tail also change the pitching moment around the neutral point. But that is besides the point: The special characteristic of the neutral point is its neutrality regarding to changes in angle of attack.
Mathematically speaking: If the slope of the pitching moment over angle of attack is zero, the reference point for this moment is the neutral point. If you pick a different point ahead of the neutral point, the slope will become negative (which characterizes a stable configuration) and vice versa. The neutral point depends on the derivative of the pitching moment over angle of attack, so the absolute value of it doesn't matter. It's the change with angle of attack that counts.
If the center of gravity coincides with the neutral point, the airplane has neutral longitudinal stability. Hence the name.
This all is valid only in the range of attached flow. If there is massive separation, all bets are off.