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Hybrid superconducting-photonic microresonators are a promising platform for realizing microwave-to-optical transduction. However, the absorption of scattered photons by the superconductors leads to unintended microwave resonance-frequency variation and line-width broadening. Here, we experimentally study the dynamics of this effect and its impact on microwave-to-optics conversion in an integrated lithium niobate–superconductor hybrid-resonator platform. We unveil an adiabatic frequency shifting of the intracavity microwave photons induced by the fast photoresponses of the thin-film superconducting resonator. As a result, the temporal and spectral responses of electro-optics transduction are modified and well described by our theoretical model. This work provides insights into the light-induced conversion dynamics that must be considered in future designs of hybrid superconducting-photonic system.