Photoluminescence of ZnMnSe/ZnSSe multiple quantum wells under a bandgap continuous wave and fs-pulsed excitations is measured in magnetic fields up to 10 T in Faraday geometry at temperatures within the range of 1.6-20 K. The measurements reveal two dominant lines in the spectra and LO-phonon replicas of the lower-energy line. The photoluminescence and time-resolved studies show dramatically different behaviour of the lines. Analysis of their properties reveals that they correspond to recombination of indirect localized excitons and indirect acceptor-bound excitons (A0X). Crossing of exciton and A0X lines because of the difference in magnitudes of their Zeeman shifts is observed. Analysis of LO-phonon replicas of photoluminescence lines provides additional evidence for strong carrier localization bound to A0X. A model of phonon-assisted recombination of indirect acceptor-bound excitons is proposed. The fitting of photoluminescence lines with this model gives the Huang-Rhys factor S ≃ 0.25 for A0X and the hole localization size ah ≃ 30 Å. Contrary to expectations the exciton magnetic polaron effect is hardly observed in these structures.