We used time resolved photoluminescence (TRPL) spectroscopy to compare the properties of magnetic polarons in two related, spatially indirect, II-VI epitaxially grown quantum dot systems. In sample A (ZnMnTe/ZnSe), the photo-excited holes are confined in the magnetic ZnMnTe quantum dots (QDs), while the electrons remain in the surrounding non-magnetic ZnSe matrix. In sample B (ZnTe/ZnMnSe) on the other hand, the holes are confined in the non-magnetic ZnTe QDs and the electrons move in the magnetic ZnMnSe matrix. The magnetic polaron formation energies, EMP, in these samples were measured from the temporal red-shift of the excitonic emission peak. The magnetic polarons in the two samples exhibit distinct characteristics. In sample A, the magnetic polaron is strongly bound with EMP = 35 meV. Furthermore, EMP has unconventionally weak dependence of on both temperature T and magnetic field Bappl. In contrast, magnetic polarons in sample B show conventional characteristics with EMP decreasing with increasing temperature and increasing external magnetic field. We attribute the difference in magnetic polaron properties between the two types of QDs to the difference in the location of the Mn ions in the respective structures.