The traditional approach of the mean-field supersaturation to kinetic description of nucleation is based on assumptions that homogeneous nucleation of overcritical particles of a new phase in a closed system occurs uniformly over the volume of the system and is synchronous with a decrease in the mean supersaturation of the metastable phase. The approximation of the mean supersaturation field also implies that the transport of molecules of the metastable phase into the growing particles of the new phase is slow and stationary. We have found in this work that, in the diffusion regime of the particle growth, the approach of the mean-field of supersaturation at the end of the first stage of formation of overcritical droplets in a supersaturated vapor requires low volatility of the condensing liquid, and in the case of the stage of nucleation of overcritical bubbles gas in a solution supersaturated with gas realizes only at extremely low solubility of gas in solution. In particular, for condensation of water vapor and degassing ethanol supersaturated by gas with moderate or high solubility at atmospheric pressure, the approximation of the mean-field supersaturation cannot be strictly justified. We demonstrated here that there are no such restrictions when using the excluded volume approach in the kinetic description of the phase transition. Along with that we have shown, that the excluded volume approach describes the processes of fast self-similar diffusion growth of particles of a new phase at the nucleation stage, leading to the formation of a cellular structure at the next stage of the phase transformation, the stage of intense decrease in the supersaturation of the metastable system.