Relatively recent experiments on the scintillation response of CsI:Tl have found that there are three main decay times of about 730 ns, 3 µs, and 16 µs, i.e. one more principal decay component than had been previously reported; that the pulse shape depends on gamma ray energy; and that the proportionality curves of each decay component are different, with the energy dependent light yield of the 16 µs component appearing to be anticorrelated with that of the 0.73 µs component at room temperature. These observations can be explained by the described model of carrier transport and recombination in a particle track. It takes into account processes of hot and thermalized carrier diffusion, electric field transport, trapping, nonlinear quenching, and radiative recombination. With one parameter set, the model reproduces multiple observables of CsI:Tl scintillation response, including the pulse shape with rise and three decay components, its energy dependence, the approximate proportionality, and the main trends in proportionality of different decay components. The model offers insights on the spatial and temporal distributions of carriers and their reactions in the track. I.