We utilized time-resolved photoluminescence (TRPL) spectroscopy to study the excitonic circular polarization (PX) from CdSe/CdMnS core/shell nanoplatelets (NPLs) with a bilayer core. This allows an extensive study of the emission dynamics as a function of magnetic field, temperature, doping concentration, and excitation wavelength. In the presence of an external magnetic field, pulsed excitation below the shell gap results in near-zero excitonic circular polarization PX at all time delays. In contrast, pulsed excitation with photon energy larger than the shell gap results in a rapid (100 ps) buildup of the excitonic circular polarization which subsequently remains constant at a level of up to 40%. We propose a model to describe the dynamics which takes into account the exchange interaction between carrier and magnetic ion (Mn) spins. The studied system exhibits a fast switchable excitonic circular polarization, implying possible applications in lasers and light emitting diodes.