We present James Webb Space Telescope MIRI data of the inner ∼3 × 2 kpc² of the galaxy IC 5063, in which the jets of a supermassive black hole interact with the gaseous disk they are crossing. Jet-driven outflows were known to be initiated along or near the jet path and to modify the stability of molecular clouds, possibly altering their star formation properties. The MIRI data, of unprecedented resolution and sensitivity in the infrared, now reveal that there are more than 10 discrete regions with outflows, nearly doubling the number of such known regions. Outflows exist near the radio lobes, at the nucleus, in a biconical structure perpendicular to the jet, and in a bubble moving against the disk. In some of them, velocities above escape velocity are observed. Stratification is also observed, with higher ionization or excitation gas attaining higher velocities. More outflows and bow shocks, found further away from the nucleus than the radio lobes, in regions without significant radio emission, reveal the existence of past or weak radio jets that interacted with the interstellar medium. The coincidence of the bow shocks with the optical extended emission line region (EELR) suggests that the jets also contributed to the gas ionization. Maps of the H₂ gas excitation temperature, T _ex, indicate that the molecular gas is most excited in regions with radio emission. There, T _ex is >100 K higher than in the EELR interior. We argue that a combination of jet-related shocks and cosmic rays is likely responsible for this excess molecular gas excitation.