On my F31 (which I no longer have) I thought doing that just put the gearbox in sport mode, but to change the engine response you still need the buttons. Need to try it in my G series sometime.
On my G20 it's the same - sport mode and S transmission mode are two separate things.
You two are right. The sports mode button does more than the shifter tilt on the F30 as well but the more aggressive gearing is usually all I need to overtake.