Energy dependence of heavy quarkonia production in hadron-nucleus collisions is studied in the framework of the Glauber-Gribov theory. We emphasize a change in the space-time picture of heavy-quark state production on nuclei with energy. Longitudinally ordered scattering of a heavy-quark system takes place at low energies, while with increasing energy it transforms to a coherent scattering of projectile partons on the nuclear target. The characteristic energy scale for this transition depends on masses and rapidities of produced particles. For J/psi, produced in the central rapidity region, the transition happens at RHIC energies. The parameter-free calculation of J/psi in dAu collisions is in good agreement with recent RHIC data. We use distributions of gluons in nuclei to predict suppression of heavy quarkonia at LHC.