  We unravel the correlated non-equilibrium dynamics of a mass balanced
Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an
imposed harmonic trap from strong to weak confinement. Regarding the system's
ground state, the competition between the inter and intraspecies interaction
strength gives rise to the immiscible and miscible phases characterized by
negligible and complete overlap of the constituting atomic clouds respectively.
The resulting dynamical response depends strongly on the initial phase and
consists of an expansion of each cloud and an interwell tunneling dynamics. For
varying quench amplitude and referring to a fixed phase a multitude of response
regimes is unveiled, being richer within the immiscible phase, which are
described by distinct expansion strengths and tunneling channels.
