Why is it advised to turn the aileron away from quartering tail-wind during taxiing?
The mnemonic that I use is, "climb into headwind, dive away from tailwind." 

To address your question. 

When the wind is a quartering tailwind, the tailwind component tends to want to lift the tail of the airplane, which could cause a prop strike or the airplane to be flipped over if the wind is strong enough. So by having the elevator all the way down, the wind hitting the tail will push the tail down instead of lifting it up.

The quartering tailwind hitting the trailing edge of the up-wind wing can lift the wing, so by diving away from the tailwind, the upwind aileron will be in the down position, which will help hold that wing down. 

With regard to the physics of how this works, it has to do with the direction in which the wind is being deflected. When wind is coming from the front (headwind) an up aileron deflects the air up and pushes the wing down, but when the wind is coming from behind the wing, such as in a quartering tailwind while taxiing, the wind would catch an up aileron and lift the wing, so it is necessary to put the aileron down, so that the wind is deflected upwards thereby pushing that wing tip down.