The decay kinetics of the excitonic emission of CdWO4 scintillators was studied under excitation by powerful 100 fs laser pulses in the band tail (Urbach) absorption region. A special imaging technique possessing both spatial and temporal resolution provided a unique insight into the Förster dipole-dipole interaction of self-trapped excitons, which is the main cause of the nonlinear quenching of luminescence in this material. In addition, the saturation of phonon-assisted excitonic absorption due to extremely short excitation pulses was discovered. A model describing the evolution of electronic excitations in the conditions of absorption saturation was developed and an earlier model of decay kinetics based on the Förster interaction was extended to include the saturation effect. Compared to the previous studies, a more accurate calculation yields 3.7 nm as the Förster interaction radius. It was shown that exciton-exciton interaction is the main source of scintillation nonproportionality in CdWO4. A quantitative description using a new model of nonproportionality was presented, making use of the corrected value of the Förster radius.