Many many years ago now JWD offered us the three basic rules of tires:
Match the hardness of a tire to how abrasive the track. More abrasive, harder tire.
Match sidewall stiffness to how hard the track. Harder track, stiffer sidewall.
and... Match air pressure to track grip. Less grip, less air pressure.
That's it about tires and what to do in a nutshell.
The rest is about how circumstances change and fine tuning to prevent or fix on track problems big and small.
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Now I'll throw in my odd logic on it bringing in 1 and 1 to get 3 as usual:.
Some logic to throw into the mix.
4 wheel drift means your left side tires have given out and the right side tires can't hold all the weight and grip expectations on them, by themselves, so you drift out to the right.
Left front tire give out and the right front tire can't hold all the weight put to it, so you push.
Left rear tire gives out and the right rear tire can hold what it needs to hold, so your loose.
That stuff together and air split is to help left side tires hold grip longer because in general less air matches up with less grip.
And you get the less grip because in general turning moves weight to the right off the left side tires.
Since the thoughts in this are about the fronts then fine tuning can come in to either free the right front up letting the left front loose grip faster/sooner or tighten the front up with less air trying to help hold grip at the left front longer.
Lots and lots of things we talk about on here all the time to fix problems or go faster are bout controlling when a left side tire weakens it's grip and how much grip it looses when you need it to loose grip.
... or it ain't because this is just IMHO and ain't necessairly right anyway. ...
So air split is just one way of many ways to control the amount of grip at the left side tires and in turn control the load on the right side tires to put them as close as possible to be running at their limit of grip, ... to be fast.
edit: That IMHO is the purpose. The why you need to do it is endless. ...