We used continuous wave photoluminescence (cw-PL) and time resolved photoluminescence (TR-PL) spectroscopy to compare the properties of magnetic polarons (MP) in two related spatially indirect II-VI epitaxially grown quantum dot systems. In the ZnTe/(Zn,Mn)Se system the holes are confined in the non-magnetic ZnTe quantum dots (QDs), and the electrons reside in the magnetic (Zn,Mn)Se matrix. On the other hand, in the (Zn,Mn)Te/ZnSe system, the holes are confined in the magnetic (Zn,Mn)Te QDs, while the electrons remain in the surrounding nonmagnetic ZnSe matrix. The magnetic polaron formation energies MP E in both systems were measured from the temporal red-shift of the band-edge emission. The magnetic polaron exhibits distinct characteristics depending on the location of the Mn ions. In the ZnTe/(Zn,Mn)Se system the magnetic polaron shows conventional behavior with MP E decreasing with increasing temperature T and increasing magnetic field B. In contrast, MP E in the (Zn,Mn)Te/ZnSe system has unconventional dependence on temperature T and magnetic field B; MP E is weakly dependent 2 on T as well as on B. We discuss a possible origin for such a striking difference in the MP properties in two closely related QD systems.