The CHandra Extended Emission Line Region Survey (CHEERS) is an X-ray study of nearby active galactic nuclei (AGN) designed to take full advantage of Chandra's unique angular resolution by spatially resolving feedback signatures and effects. In the second paper of a series on CHEERS target NGC 3393, we examine deep high-resolution Chandra images and compare them with Hubble narrow line images of [O III], [S II] and Hα, as well as previously-unpublished midultraviolet (MUV) images. We find evidence for a complex multi-phase structure in the circumnuclear ISM, with no single simple correlation between X-rays and high-ionization ([O III]/Hα-dominated) and low-ionization ([S II]-dominated) features. We also find X-ray structures ∼ 50-pc in extent, Hα evidence for gas compression, and extended MUV emission associated with the Sshaped arms that envelope the radio jets. In conjunction with existing STIS kinematics, these findings support a role for shock contributions to the feedback, driven by the radio outflows associated with the radio jets.