We investigated the electron transfer processes in methylene blue-CdTe and methylene blue-CdTe/CdSe complexes by steady state and femtosecond transient absorption spectroscopy by selective excitation of the quantum dot (QD) moiety. The ultrafast electron transfer is accelerated by the shell growth due to the separation of the charge carriers and the resulting increase of electron density in the shell. Transmission electron microscope images show that the successive addition of shell material deforms the spherical QDs until they adopt a tetrapodal shape. The increased donor-acceptor distance in the tetrapodal CdTe/CdSe QDs leads to a slower electron transfer. Photon flux dependent transient absorption measurements indicate the separation of two electrons for the QDs with a thin shell and thus demonstrate that charge carrier multiplication can be directly utilized for increased charge transfer in this type of QD hybrid system.