We present simulations of inductive helicity injection in the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI) device that treats the entire plasma volume in a single dynamic MHD model. A new fully 3D numerical tool, the PSI-center TETrahedral mesh code, was developed that provides the geometric flexibility required for this investigation. Implementation of a zero-β Hall MHD model using PSI-TET will be presented including formulation of a new self-consistent magnetic boundary condition for the wall of the HIT-SI device. Results from simulations of HIT-SI are presented focusing on injector dynamics that are investigated numerically for the first time. Asymmetries in the plasma loading between the two helicity injectors and progression of field reversal in each injector are observed. Analysis indicates cross-coupling between injectors through confinement volume structures. Injector impedance is found to scale with toroidal current at fixed density, consistent with experimental observation. Comparison to experimental data with an injector drive frequency of 14.5 kHz shows good agreement with magnetic diagnostics. Global mode structures from Bi-Orthogonal decomposition agree well with experimental data for the first four modes.