Normal.

When the engine is cold, the secondary air pump introduces more air to the exhaust to dilute the gases and results in the s2000 getting qualified as a low emissions vehicle. It turns off a few minutes after; usually when the car has had enough time to warm up.

 

I dont want to complicate things but, mine doesn't turn off couple of minutes later... i hear it all the time. It's on all the time...
Idk about when im driving on the freeway because the street sound level + soft top is too loud to tell.

And I can make the "fuel pump sound" louder by rolling the windows up or down... I guess using the battery affects this sound.