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Abstract Spillover of adsorbed species from one active site to another is a key step in heterogeneous catalysis. However, the factors controlling this step, particularly the spillover of polyatomic species, have rarely been studied. Herein, we investigate the spillover dynamics of H* and CH₃* species on a single‐atom alloy surface (Rh/Cu(111)) upon the dissociative chemisorption of methane (CH₄), using molecular dynamics that considers both surface phonons and electron‐hole pairs. These dynamical calculations are made possible by a high‐dimensional potential energy surface machine learned from density functional theory data. Our results provide compelling evidence that the H* and CH₃* can spill over on the metal surface at experimental temperatures and reveal novel dynamical features involving an internal motion during diffusion for CH₃*. Increasing surface temperature has a minor effect on promoting spillover, as geminate recombinative desorption becomes more prevalent. However, the poisoning of the active site can be mitigated by the frequent gaseous molecular collisions that occur under ambient pressure in real‐world catalysis, which transfer energy to the trapped adsorbates. Interestingly, the bulky CH₃* exhibits a significant spillover advantage over the light H* due to its larger size, which facilitates energy acquisition. These insights help to advance our understanding of spillover in heterogeneous catalysis.