Time-resolved optical spin-quantum-beat measurements performed on magnetically doped II-VI bulk semiconductors reveal an increase of the electron spin dephasing time with rising temperature typical for motional narrowing. With the dephasing being notably faster than in undoped II-VI semiconductors, the magnetic dopants must play a key role, modifying the known dephasing mechanisms and introducing new ones. Focusing on the latter, we theoretically explore the spin dephasing channel arising from magnetization fluctuations sampled by the itinerant excitons. This mechanism suffices to explain quantitatively the results of our time-resolved Faraday-rotation experiments on optically excited Cd(1-x)Mn(x)Te which we present here as a function of magnetic field, temperature and manganese dopant density. In addition to electron spin-quantum beats, some of our experiments reveal hole spin beats as well.