We observe that the wavefunction overlap of the carriers in type-IIb quantum dots can be controlled by magnetic doping and strongly depends on the excitation power density. We study epitaxially grown ZnTe/ZnSe and magnetically doped (Zn,Mn)Te/ZnSe quantum dots that show a fast and slow recombination channel at two different energies. The emission shift of the slow recombination is independent of excitation power density (Pex), whereas the fast recombination channel exhibits a larger emission shift with increasing Pex. This blue shift saturates for high Pex, however at a lower Pex and smaller maximum shift in the magnetic system compared to the nonmagnetic system. The emission wavelength immediately after pulsed excitation typically changes as a function of charge carrier density due to the spatially indirect nature of type-IIb quantum dots. As carriers increase, the confinement potential of the system is altered due to a Coulomb interaction. The magnetic system exhibits a limited change in the wavefunction overlap of the carriers for high excitation power densities which we attribute to magnetic interactions to the hole wavefunction inside the dot. This would allow for an external manipulation of the magnetic polaron binding energy through varying the excitation power density Pex in quantum dots.