In this article, we investigate the structural relaxation of lithium silicate glass during isothermal physical aging by monitoring the temporal evolution of its refractive index and enthalpy following relatively large (10–40 °C) up- and down-jumps in temperature. The Kohlrausch–Williams–Watts function aptly describes the up- and down-jump data when analyzed separately. For temperature down-jumps, the glass exhibits a typical stretched exponential kinetic behavior with the non-exponentiality parameter β < 1, whereas up-jumps show a compressed exponential behavior (β > 1). We analyzed these datasets using the non-exponential and non-linear Tool–Narayanaswamy–Moynihan (TNM) model, aiming to provide a comprehensive description of the primary or α-relaxation of the glass. This model described both up- and down-jump datasets using a single value of β ≤ 1. However, the standard TNM model exhibited a progressively reduced capacity to describe the data for larger temperature jumps, which is likely a manifestation of the temperature dependence of the non-exponentiality or non-linearity of the relaxation process. We hypothesize that the compressed exponential relaxation kinetics observed for temperature up-jumps stems from a nucleation-growth-percolation-based evolution on the dynamically mobile regions within the structure, leading to a self-acceleration of the dynamics. On the other hand, temperature down-jumps result in self-retardation, as the slow-relaxing denser regions percolate in the structure to give rise to a stretched exponential behavior.