Magnetization is induced in an ensemble of quantum dots, each charged with a single electron, when it is illuminated with a short circularly polarized light pulse that is resonant with the fundamental energy gap of the quantum dots. In this investigation, a quantum-mechanical model for the light-induced magnetization is presented. The phase of the magnetization precession as a function of the strength of the magnetic field in a Voigt geometry is in excellent agreement with experimental data measured on (In,Ga)As singly charged quantum dot ensembles. It is demonstrated that the precession of the hole in the trion plays a vital role because it determines the amplitude and phase of the magnetization precession. The model could also be easily extended to describe positively charged quantum dots. We also suggest that our theory, combined with measurements of the phase as a function of magnetic field, can be used as a technique to measure the resonant trion lifetime as a function of QD emission energy.