You shouldn't really just put on a red filter and set it to AWB, because red filter only work down to 30 or 40 feet or so. Why else all the goPro flip filter need 3 different shade of red? There is no one red filter that work on a depth so MWB is still required.
Here is some explanation of Magic filter, and at the bottom it explain filter + MWB.
http://www.uwphotographyguide.com/underwater-photography-filters
That's theory and actually pretty incorrect couple of videos with auto white balance
And another
The practical demonstration that custom white balance at all costs does not produce best results is actually in an ikelite promo video
You can see that custom white balance actually has the wrong hues
There are two parts to the white balance issue:
1. The camera doesn't just get it right
2. The water effect in terms of temperature and tint
Scubabob example is 1 above you need to start the footage with something in the frame so that the camera gets it right. Similar issue to go pro
The second case does not require custom white balance with a red filter unless you are really deep and want to try with the filter (most times results are crap regardless)
A blue water filter is usually just a mired shift with a bit of tint the net effect is to bring the camera within the range auto white balance works (up to 7000K) the shift is around 3000K. So when the color temperature goes above say 9000K your filter brings it back in range. When it is really super cool at 10000K even with the filter you are out of range so in theory you need to white balance however this usually occurs at depth where the extra stop of the filter produces footage so grainy that you tend to use a setting with 9900K and Max out the tint although most times is better to shoot black and white
If the camera is capable of finding a good white balance and the mechanism doesn't get fooled whe in water there is no benefit to use custom white balance unless the camera itself has an issue
I balance all cameras on land and then compare the difference with a shot in auto white balance most times the temperature is correct but the tint is marginally off so I set white balance to auto and shift the tint a bit to compensate. The malta video has yellow increased to +1 in auto as the sony like to push too deep blues