Understanding the dynamics of equilibration processes in quantum systems as well as their interplay with dissipation and fluctuation is a major challenge in quantum many-body theory. The timescales of such processes are investigated in collisions of atomic nuclei using fully microscopic approaches. Results from time-dependent Hartree-Fock and time-dependent random-phase approximation calculations are compared for 13 systems over a broad range of energies. The timescale for full mass equilibration (∼2×10^{-20} s) is found to be much larger than timescales for neutron-to-proton equilibration, kinetic energy, and angular momentum dissipations which are on the order of 10^{-21} s. Fluctuations of mass numbers in the fragments and correlations between their neutron and proton numbers build up within only a few 10^{-21} s. This indicates that dissipation is basically not impacted by mass equilibration, but is mostly driven by the exchange of nucleons between the fragments.