I don't know, but I hypothesize that in the way you've described it's not much different than the reason why you can be laying in bed, sleepy and sober, but in an instant, you can decide to do something active like ride a bike or work out and your brain chemistry will change to suit the new activity. The act of deciding to be active and doing something active releases a new balance of hormones and neurotransmitters, like adrenaline & whatever else, that override the cozy, sleepy state you were in prior.
The fact that you can quickly override kavas effect like that (in most circumstances) is a pretty significant difference between it and 'harder drugs'. It might even possibly be a clue that the effect kava has on your hormones and neurotransmitters more closely mimics that of similar natural body processes than other drugs do. This is not say that kava is even weak or mild compared to other drugs, it can be plenty strong, and sometimes just as strong as 'hard drugs', I think it just happens to have a chemical effect that coincidentally can be both effective and also largely suppressed fairly easily when needed. Just as it happens to be effective yet non-addictive, non-tolerance building and generally neutral to your health.
The other way kava and physical activity don't work well together, is that it can simply feel bad to do both, your stomach can be queasy and full of liquid, your whole self generally feels drawn toward simple, peaceful, quiet relaxation and enjoyment...ripping yourself out of this state can feel unpleasant and the unpleasantness becomes a distraction.