Energy absorption of xenon clusters embedded in helium nanodroplets from strong femtosecond laser pulses is studied theoretically. Compared to pure clusters we find earlier and more efficient energy absorption in agreement with experiments. This effect is due to resonant absorption of the helium nanoplasma whose formation is catalyzed by the xenon core. For very short double pulses with variable delay both plasma resonances, due to the helium shell and the xenon core, are identified and the experimental conditions are given which should allow for a simultaneous observation of both of them.