The dynamics of dications after x-ray-induced Auger decay and their probing with a delayed infrared probe pulse are theoretically investigated based on a quantum-mechanical model including all relevant electronic states for which wave-packet calculations on ab-initio potential energy curves are performed. Our results demonstrate that the yield modulated by the delay of the probe pulse contains dynamical information on the wave-packet evolution in the quasi-bound final electronic states. The Fourier transform of the calculated yield can be readily compared to experimental results [Fung et al., Nature 532, 471 (2016)] and good agreement of the main frequencies is found. Moreover, assignment of these frequencies to specific vibrational energy levels in the quasi-bound potentials is reported as well.