We consider the case, in QCD, of a single jet propagating within a strongly interacting fluid, of finite extent. Interactions lead to the appearance of a source of energy-momentum within the fluid. The remnant jet that escapes the container is analyzed along with portions of the medium excited by the jet. We study the effect of a static versus a semi-realistic expanding medium, with jets traveling inward versus outward. We consider the medium response via recoils in partonic scatterings based on a weakly-coupled description and its combination with hydrodynamical medium response based on a strongly-coupled description, followed by incorporation into a jet. The effects of these limits on the reconstructed energy, momentum and mass of the jet, as a function of the angle away from the original parton direction are studied. It is demonstrated that different flow velocity configurations in the medium produce considerable differences in jet observables. This work highlights the importance of accurate dynamical modeling of the soft medium as a foundation on which to calculate jet modification, and casts skepticism on results obtained without such modeling.