A wide variety of compositions adopt the isometric spinel structure (AB2O4), in which the atomic-scale ordering is conventionally described according to only three structural degrees of freedom. One, the inversion parameter, is traditionally defined as the degree of cation exchange between the A- and B-sites. This exchange, a measure of intrinsic disorder, is fundamental to understanding the variation in the physical properties of different spinel compositions. Based on neutron total scattering experiments, we have determined that the local structure of Mg1-xNixAl2O4 spinel cannot be understood as simply being due to cation disorder. Rather, cation inversion creates a local tetragonal symmetry that extends over sub-nanometer domains. Consequently, the simple spinel structure is more complicated than previously thought, as more than three parameters are needed to fully describe the structure. This new insight provides a framework by which the behavior of spinel can be more accurately modeled under the extreme environments important for many geophysics and energy-related applications, including prediction of deep seismic activity and immobilization of nuclear waste in oxides.