Glassy polymers are often used for gas separations because of their high selectivity. Although the dual‐mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time‐dependent permeation of N2 and CO2 through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time‐dependent permeation data for both gases in the presteady‐state and steady‐state regimes show that both single‐ and dual‐mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment‐sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.