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The photoluminescence of annealed Cd\(_x\)Zn\(_{1-x}\)Se quantum dots (QDs) under the influence of an external magnetic field has been studied in this paper. Post-growth annealing was performed for different annealing times. Above a critical annealing time, the QD luminescence shows a pronounced red-shift of the Zeeman split magnetic subcomponents. This observation is in contrast to the blue-shift caused by the diamagnetic behavior that is usually observed in non-magnetic QDs. We attribute our finding to the paramagnetism caused by the mixing of heavy and light hole states. Hence, post-growth thermal annealing treatment might be employed to render undoped epitaxial QDs intrinsically magnetic in a controlled manner. Two theoretical models were developed: a few-particle model to account for excitonic complex effects and a multiband calculation that describes the valence band hybridization. Contrasting the two models allowed us to unambiguously elucidate the nature of such an effect.