The relaxation processes induced by exposure of the Ar matrices doped with CH4 (0.1–10%) to an electron beam were studied with a focus on the dynamics of radiolysis products—H atoms, H2 molecules, CH radicals, and energy transfer processes. Three channels of energy transfer to dopant and radiolysis products were discussed, including free charge carriers, free excitons and photons from the “intrinsic source” provided by the emission of the self-trapped excitons. Radiolysis products along with the total yield of desorbing particles were monitored in a correlated manner. Analysis of methane transformation reactions induced by free excitons showed that the CH radical can be considered a marker of the CH3 species. The competition between exciton self-trapping and energy transfer to the dopant and radiolysis products has been demonstrated. A nonlinear concentration behavior of the H atoms in doped Ar matrices has been established. Real-time correlated monitoring of optical emissions (H atom and CH3 radicals), particle ejection, and temperature revealed a nonmonotonic behavior of optical yields with a strong luminescence flash after almost an hour of exposure, which correlated with the explosive pulse of particle ejection and temperature. The connection of this phenomenon with the processes of energy transfer and recombination reactions has been established. It is shown that the delayed explosive ejection of particles is driven by both the recombination of H atoms and CH3 radicals. This occurs after their accumulation to a critical concentration in matrices at a CH4 content C ≥ 1%.