The AX100 is a great camera, one I was seriously looking at myself. However as you can see it doesn't have the best White Balance underwater, which is a shame.
Using any lights underwater? = NO Filter and set the WB to the Kelvin of the lights (if you can, otherwise use 'shade' is my preference)
Using only the ambient light? = Use Filters and CWB/MWB or just MWB on its own, if camera is good (which the AX100 isn't)
I wouldn't use AWB, incase the ambient light interferes and causes a WB shift, I would lock it to one of the presents (Custom like shade, indoors etc) which is the most pleasing to the eye.
You can get very technical, by using lights with a filter on the camera, but they you need the reserve filter on the lights ('Cyan Filters').
Pete's guide is excellent, with a lot of work gone into it, to get pleasing colours from the AX100, but is aimed at only ambient lit shots.