We study a homogeneously doped 70-nm-thick ZnSe epilayer with fluorine donor concentration of about 1015cm-3, grown by molecular beam epitaxy on top of a 20-nm-thick Zn0.92Mg0.08Se layer, which prevents carrier diffusion into the GaAs substrate with a smaller band gap. The sample is placed in an optical cryostat with a superconducting split-coil magnet. Pump-probe time-resolved Kerr rotation was used to study the dynamics of the donor-bound electron spins. Electron spin coherence is generated by a train of circularly polarized pump pulses of 1.5 ps duration emitted by a mode-locked Ti: Sapphire laser operating at a repetition period TR = 13.2 ns. The excited spin coherence is measured by the Kerr rotation of the linearly-polarized probe pulses in a perpendicular applied magnetic field. The Larmor precession frequency serves as a measure for the total magnetic field exerted onto the electron spins and, surprisingly, does not increase linearly with the applied field, but shows a step-like behavior with pronounced plateaus, given by multiples of the laser repetition rate. Plateaus in precession frequency vs. magnetic field. Dependence of precession frequency ω (given in units of laser repetition rate) on applied field in absolute units (bottom) and units of (top). The total magnetic field is given on the right axis in units of B0. Power dependence of the local field. Laser power dependence of induced Overhauser field (BN) on the applied magnetic field (BX) in absolute units (bottom) and units of B0 (top). It demonstrates a smooth transition between positive and negative detuning that is controlled by the laser power.