  We investigate the nonequilibrium quantum dynamics of a single and two heavy
fermionic impurities being harmonically trapped and repulsively interacting
with a finite ensemble of majority fermions. A quench of the potential of the
majority species from a double-well to a harmonic trap is applied, enforcing
its counterflow which in turn perturbs the impurities. For weak repulsions it
is shown that the mixture undergoes a periodic mixing and demixing dynamics,
while stronger interactions lead to a more pronounced dynamical spatial
separation. In the presence of correlations the impurity exhibits an expansion
dynamics which is absent in the Hartree-Fock case resulting in an enhanced
degree of miscibility. We generalize our results to different impurity masses
and demonstrate that the expansion amplitude of the impurity reduces for a
larger mass. Furthermore, we showcase that the majority species is strongly
correlated and a phase separation occurs on the two-body level. Most
importantly, signatures of attractive impurity-impurity induced interactions
mediated by the majority species are identified in the time-evolution of the
two-body correlations of the impurities, a result that is supported by
inspecting their spatial size.
