We discuss time reversal ($T$) violation in neutrino oscillations in generic new physics scenarios. A general parametrization is adopted to describe flavor evolution, which captures a wide range of new physics effects, including nonstandard neutrino interactions, nonunitarity, and sterile neutrinos in a model-independent way. In this framework, we discuss general properties of time reversal in the context of long-baseline neutrino experiments. Special attention is given to fundamental versus environmental $T$ violation in the presence of generic new physics. We point out that $T$ violation in the disappearance channel requires new physics, which modifies flavor mixing at neutrino production and detection. We use time-dependent perturbation theory to study the effect of nonconstant matter density along the neutrino path and quantify the effects for the well-studied baselines of the DUNE, T2HK, and T2HKK projects. The material presented here provides the phenomenological background for the model-independent test of $T$ violation proposed by us in [T. Schwetz and A. Segarra, Model-Independent Test of $T$ Violation in Neutrino Oscillations, Phys. Rev. Lett. 128, 091801 (2022).].