Vacancy-ordered double perovskite Cs₂SnCl₆ has attracted considerable attention due to its important application prospects in the fields of luminescence and display. However, the theoretical mechanisms underlying the emissions at 570 nm, 615 nm, and 705 nm arising from doping with Te⁴⁺, Sb³⁺, and La³⁺ ions, respectively, remain unclear, which hinders further optoelectronic applications of this material. To address this issue, this study systematically investigated the excited-state behavior of charge carriers and the formation mechanism of defect-bound excitons in Cs₂SnCl₆ doped with Te⁴⁺, Sb³⁺, and La³⁺ ions, based on first-principles calculations. Using the ΔSCF method to simulate excited states, it was found that no intrinsic self-trapped exciton exists in the perfect crystal. After doping, the introduced Te_Sn and Sb_Sn defects were found to induce hole and electron localization along with octahedral distortion under excited-state conditions, forming defect-bound excitons. The calculated PL photon energies were 2.255 eV and 2.131 eV, respectively, in good agreement with the experimental values of 2.175 eV and 2.016 eV. For the La³⁺-doped system, the La_Sn defect alone did not generate self-trapped excitons; instead, the complex defect La_Sn + VCl induced octahedral distortion and created a hole-localized state, yielding an emission at 1.63 eV, which closely matched the experimentally observed emission at 1.756 eV. This work reveals the physical origin of the photoluminescence in Cs₂SnCl₆ doped with Te⁴⁺, Sb³⁺, and La³⁺ ions, providing a theoretical basis for optical regulation and optoelectronic applications of zero-dimensional perovskites.