Your white balance is off because the 10-stop ND filter has a warming effect (my B+W 77mm and Schneider 82mm 10-stoppers do).
That doesn't sound very "neutral" at all! Do all 10-stoppers have that problem? And if so, why?
I think so.
Lee doesn't seem to publish transmission curves, but for the Big Stopper they warn, "Use of the Big Stopper may result in a slight colour cast.
B+W does publish transmission curves (one reason I like them - you know, up front, what you're getting), and it's clear that with the 110 (10-stop) and to a lesser degree with the 106 (6-stop) filter, there's increased transmission in the red area of the spectrum. B+W calls this out in their description of the 106 stating, "Because of its higher transmission in the red beyond 660 nm, this filter brings a slight warm tone to color photographs. If this effect is undesirable, a B+W UV-/IR-Blocking Filter 486 in front of the neutral density filter (not behind it!) remedies that situation.
" For the 10-stop filter, they indicate that the warm tone is slightly stronger than with the ND 106.
You can see the warmer tone below, top shot is no filter, bottom is the 82mm 10-stop ND from Schneider Optics (parent company of B+W and the only 82mm screw-in 10-stop filter available, AFAIK). As you can see, I use the 10-stop to blur out the people walking through the shot, cars going by, etc.