We demonstrate that coupled electronic and nuclear fluxes in molecules can strongly depend on the initial state preparation. Starting the dynamics of an aligned D2+ molecule at two different initial conditions, the inner and the outer turning points, we observe qualitatively different oscillation patterns of the nuclear fluxes developing after 30 fs. This corresponds to different orders of magnitude bridged by the time evolution of the nuclear dispersion. Moreover, there are attosecond time intervals within which the electronic fluxes do not adapt to the nuclei motion depending on the initial state. These results are inferred from two different approaches for the numerical flux simulation, which are both in good agreement.