The manipulation of distortions in perovskite structures is critical to tailoring the properties of these materials for a variety of applications. Here we demonstrate a violation of established octahedral tilt rules in the double perovskite analogue (NH4)2SrFe(CN)6·2H2O. The forbidden tilt pattern we observe arises through coupling to hydration-driven Jahn-Teller-like distortions of the Sr coordination environment. Access to novel distortion mechanisms and the ability to switch these distortions on and off through chemical modification fundamentally expands the toolbox of techniques available for engineering symmetry-breaking processes in solid materials.