In Zn1-xMnxSe/(Zn,Be)Se quantum wells with x<0.035, nonthermalized Mn2+ ions demonstrate in spin-flip scattering spectra multiple Stokes and anti-Stokes transitions whose absolute energies deviate by up to 20% from each other. This asymmetry is tuned significantly by the optical power density, magnetic field direction, and Mn ion concentration. The nonequidistant Mn2+ spin transitions are modeled by the Zeeman splitting and quadrupolar crystal-field components taking values of up to 7 GHz. We suggest that nonequilibrium carriers dynamically polarize the Mn-ion spins so that they occupy levels with positive and negative spin projection numbers giving rise to asymmetric spin transitions.