The boost bottle works by allowing some of the charge that would otherwise get sent back through the carby to instead run into the bottle due to the inertia of the incoming charge. This means that it doesn't get reflected back through the carb past the needle and jet, thereby enrichening the air/fuel mix.
Essentially, any charge that gets reflected back through the carby by the closed reed valve ends up passing the needle and jet three times instead of once.
1st - being drawn in through the carb
2nd - being reflected back through the carb by the closed reed valve
3rd - being drawn back through the carb when the reed valve opens again.
So, basically at the rev range where the boost bottle is apparently giving a "boost" it's partially because it's leaning the mix out (or more accurately, it's reducing how much the mix is being made richer by reducing how much of the charge passes backwards through the carby when the reed valve closes.
You could basically get the same result by changing your carb needle. Or more to the point, you should probably change your carb needle if you add a boost bottle so it doesn't lean out at the revs where the boost bottle is doing it's thing (which depends on what volume it has).
That's how I understand it, but I could be wrong.