The kinetic Boltzmann equation is used to model the non-equilibrium ionization phase that initiates the evolution of atomic clusters irradiated with single pulses of intense vacuum ultraviolet (VUV) radiation. The duration of the pulses is ≤50 fs and their intensity in the focus is ≤10¹⁴ W cm⁻². This statistical model includes various processes contributing to the sample dynamics at this particular radiation wavelength, and is computationally efficient also for large samples. Two effects are investigated in detail: the impact of the electron heating rate and the effect of the plasma environment on the overall ionization dynamics. The results for the maximal ion charge, the average ion charge and the average kinetic energy per ion are compared to the experimental data obtained at the free-electron-laser facility FLASH at DESY. Our analysis confirms that the dynamics within the irradiated samples is complex, and the total ionization rate is the resultant of various processes. In particular, within the theoretical framework defined in this model, the high-charge states as observed in the experiment cannot be obtained with the standard heating rates derived with Coulomb atomic potentials. Such high-charge states can be created with the enhanced heating rates derived with the effective atomic potentials. The modification of ionization potentials by plasma environment is found to have less effect on the ionization dynamics than the electron heating rate. We believe that our results are a step towards better understanding the dynamics within the samples irradiated with intense VUV radiation.