• Adding air to Neutral is also adding a high frequency, a little bit of hissing sound. If you keep the air on the tone and add twang, that hissing sound will be amplified.
• Some times there is air in Neutral where you don't want it. That's what the other part is about: twanging can also be used as a method to get rid of the air.
I see how it may seem contradictory, but it really isn't!
Twang is an interesting component of the singing technique, that can be used to achieve many MANY different goals. The first part is about amplifying the frequency of the airy effect, the second is about helping the vocal cords to compress a little more, so that they don't let out the exrtra air.
Am I making sense…?