There are 3 components responsible for correct exposure.
1. Aperture
2. Shutter Speed
3. ISO
There is NO correct set of three that will make a correct exposure. For example, lets say you are running f4 @ 125th and 200 iso. The EXACT same exposure can be f4 @ 250th and iso 400 or f2.8 @ 250th and iso 200, or f2.8 @ 125th and 400 iso. All of them will result in the same exposure, but completely different photographs or video due to the ancillary effects of each of the three components.
The three components form a triangle of exposure that when balanced equate to proper exposure. If you close the aperture (higher number), less light gets in so you must either slow the shutter speed to allow more time for the light to hit the film/sensor or raise the iso which increases the sensitivity to light. Similarly, if you raise the shutter speed, you must either open the aperture to allow more light in or raise the iso to make the film/sensor more sensitive to the light.
Each of the three also contributes its own aspects into the photo(video)
1. Aperture - this controls depth of field. The smaller the hole in the aperture, the larger range of depths that will be in the best focus.
2. Shutter speed - This controls the ability to stop motion. The longer the shutter is open, the longer the time that light can move on the sensor. This causes motion blur in stills and video. Conversely high or fast shutter speeds reduce or virtually eliminate motion blur.
3. ISO - This controls the sensitivity of the capturing element (film or sensor). The higher the ISO rating the more grain and noise that will be present in an image or video. In virtually all circumstances the lowest ISO rating you can use is the most desirable one however there are artistic aspects to allowing some noise.
The aperture is fixed at f2.8 for the Phantom's camera and can not be changed without replacing the lens. Therefore you can only control the other two, shutter speed and iso. So when you put the ND filter in front of the lens, its the equivalent to closing the aperture. That means either the shutter speed must slow or you must increase the ISO, or both to maintain proper exposure. Most put the ND on so they can reduce the shutter speed.
A note on shutter speed. Since this is really the only artistic component within our control on the phantom, its the one people desire to change. Since we can't lower the ISO past a certain point nor can we close the aperture, our alternative is to use ND filters. These, as I stated above, decrease light flowing through the lens allowing the shutter speed to be slowed. This, also as explained, increases motion blur. In video, this can be desirable. A slight motion blur lends a cinematic quality to video that is akin to what is natural in film. Video shot with a high shutter speed has little motion blur and appears slightly harsh or overly alien to many. It is, of course, an artistic choice.
For DSLRs ND filters are typically used to allow opening the aperture thus decreasing the depth of field. This allows us to have a crisp subject and throw the background out of focus yielding a nice boke affect.
This is an example of using an ND on a DSLR. In this photo, I used an ND8 (IIRC) to reduce the light entering the lens. This allowed me to open the aperture so that the background was out of focus while my granddaughter remained sharp:
The same shot without the ND filter on it had the background leaves and branches more in focus. This created a visual distraction in the image and reduced the subject's presence in the photo.
So, ND filters do not themselves control exposure. They allow us to simulate changing aperture so that we can change shutter speed to simulate motion blur. If you have the camera in auto, placing an ND on the lens will cause it to automatically change settings and the apparent exposure of the image will remain virtually unchanged. Its when the bird or subject begin to move rapidly that the effect of the ND will exhibit itself.
Hopefully this will help you understand just what the ND filters actualy do as they are generally used differently when placed on the Phantom and on a DSLR.