A comparative analysis of the kinetic properties of intracenter 3d luminescence of Mn²⁺ ions in the dilute magnetic superconductors Cd_1-xMn_xTe and Cd_1-x-yMn_xMg_yTe is carried out. The influence of relative concentrations of the cation components on the position of the intracenter luminescence peak indicates that the introduction of magnesium enhances crystal field fluctuations. As a result, the processes facilitating nonlinear quenching of luminescence are suppressed. The kinetics of 3d-luminescence quenching in Cd_1-xMn_xTe are accelerated considerably upon elevation of optical excitation level due to the evolution of cooperative processes in the system of excited manganese ions.