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Three Tidal Disruption Event candidates (AT2019dsg, AT2019fdr, and AT2019aalc) have been associated with high-energy astrophysical neutrinos in multimessenger follow-ups. In all cases, the neutrino observation occurred$\mathit{}(100)$days after the maximum of the optical-ultraviolet (OUV) luminosity. We discuss unified fully time-dependent interpretations of the neutrino signals where the neutrino delays are not a statistical effect, but rather the consequence of a physical scale of the post-disruption system. Noting that X-ray flares and infrared (IR) dust echoes have been observed in all cases, we consider three models in which quasi-isotropic neutrino emission is due to the interactions of accelerated protons of moderate, medium, and ultra-high energies with X-rays, OUV, and IR photons, respectively. We find that the neutrino time delays can be well described in the X-ray model assuming magnetic confinement of protons in a calorimetric approach if the unobscured X-ray luminosity is roughly constant over time, and in the IR model, where the delay is directly correlated with the time evolution of the echo luminosity (for which a model is developed here). The OUV model exhibits the highest neutrino production efficiency. In all three models, the highest neutrino fluence is predicted for AT2019aalc, due to its high estimated supermassive black hole mass and low redshift. All models result in diffuse neutrino fluxes that are consistent with observations.