My interpretation may differ from Mr.Nodera and the Rajeffs among others who employ it, but here goes:
The vee grip does not rely on the meat of the thumb to flex the rod as with the standard thumbs up grip, but instead uses the crotch of the hand between the thumb and index finger at the base to cradle the rod.
The back of the hand is turned to face you and the palm does the pushing on the rod.
My preference is for the index finger to open and point upward a little, letting the middle & ring fingers become the operative fingers for gripping the cork in conjunction with the thumb.
Therefore the rod handle contacts the index finger, the palm at the base of the index finger, across the hollow middle of the palm and nestles in the cleavage at the heel of the palm between the meat of the thumb muscle and the karate chop muscle.
The rod has a huge area of contact as a result. The hollow in the middle of the palm is in-line with the wrapping of fingers and thumb, just about everything else is touching cork.
The forward cast begins with a pulling motion from the backcast but soon becomes a push about mid-way. At that point the veegrip with the palm facing away puts a huge bend in the bottom of the rod which is the potential for the upcoming power snap to release the beast into the line.
I can push much more potential energy into the blank with a vee grip, particularly when spey casting. It does however seem natural and advantageous for overhead casting the Atlantis as well, and you may find this to be the case as well.
When you try it, give it some time. The hand will naturally seek it's comfort zone and if it's like my hand it really feels comfortable in that position.
I also noticed that when I go cast my trout single hander for practice after about 100 casts my hand naturally seeks to swivel palm forward to reduce the strain on the base of the thumb.
Another observation is that when backhand casting in a crosswind the hand settles on a knuckle forward position but with the same contact points on the hand-cork. In effect this is 180 degrees from the strong side vee grip, a reverse vee grip.
I will show you at Boneclave if interested.