This supplementary document provides a comprehensive explanation of the coupled rate and transport model used to calculate the scintillation dynamics in Ce-doped CLLBC crystals. The model includes a set of partial differential equations that describe the behavior of charge carriers, excitons, and their interactions within the crystal lattice. These equations account for key processes such as diffusion, trapping, recombination, and nonlinear quenching. Details on parameter selection, including energy loss rates for neutron and gamma excitation, are presented.