Yes it does, but that's because it's registering too much GB so it over compensates R. The filter sorta tempers it if the right WB neutral reflective surface is used.
Roy,
I helped out a guy on this issue on his CX earlier this year. The best way is probably still to use a 18% gray card. You can use the sun by zooming in a bit, but make sure it fills the screen over 50%. Most important, these little camcorders have only 10000k which is why I recommend MWB every 2 meters of depth change and not every 10m, once you go past 10m. The WB sensor is overwhelmed by the huge lack of R.
I would use the offset sparingly but try setting it to -2 or 3. However don't go nuts on the WB Shift.
If that doesn't work, try MWB every meter. The guy did that and it worked well, albeit a big PITA!
Looking at your pic again, you have lights on with your filter? Is that right?