That's a great question! As with any rpg, a lot is open to player interpretation, but one example of Air warping in either dimension would be to rework the sounds from a hostile acquaintance's mouth, to be friendly, or white noise, or even silence. As a Strictness effect in That dimension, you can bind air by subjecting a supernatural flying effect to the laws of reality. Binding Air in This dimension would be something more prosaic, like persuading someone to leave the window open for healthful fresh air (and perhaps later an opportunity for escape.)

I do like how you picked up on the natural duality of the game, tho I did find in playtesting that it's difficult to enforce connections unless you take turns between dimensions instead of randomizing. I think it makes for a more artistic story if you connect scenes between dimensions, but I've found that that's also often beyond the ability of novices to role-playing. It's definitely something to encourage tho!