Hybrid ferromagnet-semiconductor systems possess new outstanding properties, which emerge when bringing magnetic and semiconductor materials into contact. In such structures, the long-range magnetic proximity effect couples the spin systems of the ferromagnet and semiconductor on distances exceeding the carrier wave function overlap. The effect is due to the effective p-d exchange interaction of acceptor-bound holes in the quantum well with d-electrons of the ferromagnet. This indirect interaction is established via the phononic Stark effect mediated by the chiral phonons. Here, we demonstrate that the long-range magnetic proximity effect is universal and observed in hybrid structures with diverse magnetic components and potential barriers of various thicknesses and compositions. We study hybrid structures consisting of a semimetal (magnetite Fe3O4) or dielectric (spinel NiFe2O4) ferromagnet and a CdTe quantum well separated by a nonmagnetic (Cd,Mg)Te barrier. The proximity effect is manifested in the circular polarization of the photoluminescence corresponding to the recombination of photoexcited electrons with holes bound to shallow acceptors in the quantum well induced by magnetite or spinel itself, in contrast to interface ferromagnet in case of metal-based hybrid systems. A nontrivial dynamics of the proximity effect is observed in the studied structures due to recombination-induced dynamic polarization of electrons in the quantum well. It enables the determination of the exchange constant Δexch ≈ 70μeV in a magnetite-based structure. The universal origin of the long-range exchange interaction along with the possibility of its electrical control offers prospects for the development of low-voltage spintronic devices compatible with existing solid-state electronics.