Dopant-carrier magnetic exchange interactions in semiconductor nanostructures give rise to unusually large Zeeman splittings of the semiconductor band levels, raising possibilities for spin-based electronics or photonics applications. Here we evaluate the recently highlighted possibility of confinement-induced kinetic s-d exchange coupling in doped ZnSe/CdSe inverted core/shell nanocrystals. Magneto-optical studies of a broad series of Co(2+)- and Mn(2+)-doped core, inverted core/shell, and isocrystalline core/shell nanocrystals reveal that the dominant spectroscopic effects caused by CdSe shell growth around doped ZnSe core nanocrystals arise from hole spatial relaxation, being essentially independent of the electron-dopant interaction or the heterointerface itself. The general criteria for observation of kinetic s-d exchange coupling in doped nanocrystals are discussed in light of these results.