<p>Cryogenic thermal cycling (CTC) can alter the mechanical properties of metallic glasses (MGs) by inducing different responses of MGs from rejuvenation to relaxation. The distinction in mechanism between these responses remains unclear, which makes it difficult to achieve control over them. In this study, molecular dynamics simulations of La₆₀Ni₁₅Al₂₅ metallic glass, spanning seven orders of magnitude in cooling rate, are employed to systematically elucidate the structural origins that distinguish rejuvenation from other energy-state responses during CTC. We find that both rejuvenation and relaxation processes exhibit potential-energy trajectories that conform to the Kohlrausch-Williams-Watts (KWW) equation. The distinction between them lies in the evolution of medium-range order: relaxation proceeds through atomic-level cluster rearrangements that collectively distort the existing framework, whereas rejuvenation involves progressive, edge-to-center dissociation of a stable framework and more closely resembles β-relaxation. These distinct pathways can be captured by a single structural control parameter, the average topological connectivity 〈<i>k</i>〉 of fivefold-centered clusters. A threshold at 〈<i>k</i>〉 ≈ 4 defines the transition from rejuvenation (〈<i>k</i>〉 &gt; 4) to relaxation (〈<i>k</i>〉 &lt; 4) responses of MGs to CTC, offering a simple descriptor for predicting and modulating energy-state evolution in metallic glasses.</p>