We show that a weak external magnetic field affects significantly nonequilibrium quasiparticle (QP) distributions under the conditions of the inverse proximity effect, using the single-electron hybrid turnstile as a generic example. Inverse proximity suppresses the superconducting gap in superconducting leads in the vicinity of turnstile junctions, thus, trapping hot QPs in this region. An external magnetic field creates additional QP traps in the leads in the form of vortices or regions with a reduced superconducting gap resulting in the release of QPs away from the junctions. We present clear experimental evidence of the interplay of the inverse proximity effect and magnetic field revealing itself in the superconducting gap enhancement and significant improvement of the turnstile characteristics. The observed interplay and its theoretical explanation in the context of QP overheating are important for various superconducting and hybrid nanoelectronic devices, which find applications in quantum computation, photon detection, and quantum metrology.