We apply the Monte Carlo wave-packet approach to study the interatomic Coulombic decay (ICD) dynamics of neon dimers after removing a 2s electron from one of the Ne atoms by one-photon absorption from an XUV pulse. This method reproduces well both the lifetime for the 2s inner-valence vacancy in Ne 2 + (2s −1) and the kinetic energy release (KER) spectra for the coincident Ne + and Ne 2+ fragments following triple ionization, i.e., two photoionizations and one ionization via ICD, of Ne 2 measured in an XUV-pump-XUV-probe experiment [K. Schnorr et al., Phys. Rev. Lett. 111, 093402 (2013)]. Comparisons between the calculated and measured nuclear KER spectra give physical insights in the considered process. For example, an analysis of the ratios between the low-and high-energy peaks in the nuclear KER spectra for large delays provides an estimate of the photoionization cross sections for removing a 2p electron from the excited states in Ne 2 + (2s −1). Such comparisons also allow an estimate for the ICD rates for the 2s inner-valence vacancy in the single-site two hole state in Ne 2 2+ (2s −1 2p −1). Finally, the influence of photon statistics of the free electron laser pulses on the nuclear KER spectra is considered.