Set your pumphead for presta. No adapter is needed. Unscrew the knurled nut a couple of turns, and tap it to make sure it is not jamed shut. Put the pump on and pump to the desired pressure. Pull the pump off, screw the knurled nut tight and replace the cap.

Yes there is an aluminium adapter in the rim so that a schrader tube can be used in an emergency. Prestas work so much better tho--for example when putting tube back on rim the nut on the presta stem properly locate the stem, and prevents it from being pushed in when first inflating the tire.