In this paper, the secondary emission of different (Zn,Cd,Mn)Se/ZnSe and ZnSe/(Zn,Mn)Se quantum structures and (Zn,Mn)Se layers is studied under resonant excitation of the energetically lowest exciton state. A pronounced Stokes satellite is found arising from the exciton-induced spin-flip of anti-ferromagnetically aligned Mn2+ pairs. From the Stokes shift, the nearest-neighbor Mn2+-Mn2+ exchange constant is precisely determined to J(1)/k(B) = (- 12.8 +/- 0.2) K for (Zn,Mn)Se. An incorporation of 15% Cd does not change this value within the experimental accuracy.