One of the more promising observables to probe the high energy regime of the QCD dynamics in the future Electron - Ion Colliders (EIC) is the exclusive vector meson production cross section in coherent and incoherent interactions. Such processes measure the average spatial distribution of gluons in the target as well the fluctuations and correlations in the gluon density. In this paper we present a comprehensive analysis of the energy, photon virtuality, atomic number and momentum transfer dependencies of the coherent and incoherent cross sections considering two different models for the nuclear profile function. In particular, we present the predictions of the hot - spot model, which assumes the presence of subnucleonic degrees of freedom and an energy-dependent profile. Our results indicate that the analysis of the ratio between the incoherent and coherent cross sections and the momentum transfer distributions in the future EIC can be useful to constrain the description of the hadronic structure at high energies. (C) 2019 Elsevier B.V. All rights reserved.