Oxide heterointerfaces constitute a rich platform for realizing novel functionalities in condensed matter. A key aspect is the strong link between structural and electronic properties, which can be modified by interfacing materials with distinct lattice symmetries. Here, we determine the effect of the cubic-tetragonal distortion of SrTiO₃ on the electronic properties of thin films of SrIrO₃, a topological crystalline metal hosting a delicate interplay between spin-orbit coupling and electronic correlations. We demonstrate that below the transition temperature at 105 K, SrIrO₃ orthorhombic domains couple directly to tetragonal domains in SrTiO₃. This forces the in-phase rotational axis to lie in-plane and creates a binary domain structure in the SrIrO₃ film. The close proximity to the metal-insulator transition in ultrathin SrIrO₃ causes the individual domains to have strongly anisotropic transport properties, driven by a reduction of bandwidth along the in-phase axis. The strong structure-property relationships in perovskites make these compounds particularly suitable for static and dynamic coupling at interfaces, providing a promising route towards realizing novel functionalities in oxide heterostructures.