Recent experiments have investigated the dissociative ionization of NaI and CsI, each aggregated with a molecule of acetonitrile CH3CN, using two femtosecond laser pulses. The first, the pump pulse, excites the NaI or CsI diatom to a dissociative state. The second, the probe pulse, then ionizes the sodium or cesium atom after a variable delay time, and the resulting ion is detected. In the case of NaI, the ion signal is characterized by a single maximum. For CsI, however, an oscillatory signal is observed. By performing two-dimensional wave packet propagations, we are able to reproduce this behavior, which can be explained using simple physical arguments.