The effects of postcollision interaction (PCI) in the time evolution of photoinduced Auger decay, assisted by a terahertz (THz) field, is theoretically investigated. We propose a time-dependent model which is based on the quantum-mechanical description of the photoinduced Auger process and quasiclassical description of the PCI. The suggested model is used for calculating the PCI distortion of the Auger spectrum at different temporal overlaps of the exciting extreme ultraviolet pulse and the streaking THz pulse.