Magneto-photoluminescence experiments were carried out on self-assembled quantum dots (QDs) fabricated in the form of two adjacent QD layers separated by a thin barrier. A strong PL peak is observed in this double-layer QD system, which is identified as the ground state transition. The PL peak exhibits a large Zeeman shift, characteristic of structures involving diluted magnetic semiconductors (DMSs) when an external magnetic field is applied. However, the dependence of the PL intensity on magnetic field shows an entirely unexpected behavior in this double-layer QD structure. In contrast to typical behavior of many low-dimensional DMS systems, where the application of a magnetic field B dramatically increases the PL intensity, in double-layer structures described above we observe a striking decrease of the PL intensity as a function of B. This effect indicates carrier tunneling from CdSe to CdMnSe dots as the band edges of CdMnSe are Zeeman-shifted, thus increasing the exciton probability in the DMS QDs.