Realistic simulations of current ultracold atom experiments in optical lattices show that the ramping up of the optical lattice is significantly nonadiabatic, implying that experimentally prepared Mott insulators are not really in the ground state of the atomic system. The nonadiabaticity is even larger in the presence of a secondary quasiperiodic lattice simulating "disorder". Alternative ramping schemes are suggested that improve the adiabaticity when the disorder is not too large.