Unlike the extensively studied, spatially direct, quantum dots (QDs) with type-I band alignment where both electrons and holes are confined in the QD, in ZnTe QDs embedded in a (Zn,Mn)Se matrix only the holes are confined in the QDs. This spatially indirect type-II system provides unexplored opportunities to control the magnetic interactions between the hole spins in the nonmagnetic QDs and the spins of the magnetic ions in the matrix. Photoluminescence (PL) was excited either with photons of energy 3.06 eV [above band gap of the (Zn,Mn)Se matrix] or with photons of energy 2.54 eV [below the (Zn,Mn)Se band gap]. In the presence of an external magnetic field, the saturation red shift of the PL peak under 2.54 eV excitation exhibits an up to three-fold increase compared to the shift observed with 3.06 eV excitation. This increase is attributed to multiple hole occupancy of the QDs and the resulting increased penetration of the hole wavefunction tail further into the (Zn,Mn)Se matrix. The proposed model is supported by calculations which include the hole-hole Coulomb interactions as well as the hole-Mn spin exchange interactions.