Kinetic equations are used to model the dynamics of Xe clusters irradiated with short, intense vacuum-ultraviolet pulses. Various cluster size and pulse fluences are considered. It is found that the highly charged ions observed in the experiments are mainly due to Coulomb explosion of the outer cluster shell. Ions within the cluster core predominantly recombine with plasma electrons, forming a large fraction of neutral atoms. To our knowledge, our model is the first and only one that gives an accurate description of all of the experimental data collected from atomic clusters at 100 nm photon wavelength.