Magneto optical micro-spectroscopy allowed us to access the magnetic field dependency of the photoluminescence of Cd(Mn)Te/ZnTe single quantum dots. We report a strongly non-linear behavior of the exciton and biexciton energies as a function of magnetic field which clearly differs from the expected and usually observed giant Zeeman effect. We demonstrate that the existence of a positive feedback loop between photocarriers and Mn spins results in heating the Mn system and can explain the observed phenomenon. This shows that controlling the coupling of the dot with its environment is a corner stone to achieve spin manipulation in quantum dots.