Launched in October 2023, the Psyche spacecraft is en route to the asteroid (16) Psyche to study its exposed nickeliron core, relying primarily on its cold gas thrusters and reaction wheel assemblies for attitude control. The Guidance, Navigation, and Control (GN&C) team at the Jet Propulsion Laboratory (JPL) previously reported the linear stability values for these systems, showing the cold gas system (CGS) controller with a gain margin of 13.31 dB and phase margin of 74.4°, and the reaction wheel (RWA) controller with a gain margin of 13 dB and phase margin of 35.2°. However, these margins had not been verified against the spacecraft's nonlinear time-domain dynamics. This work addresses the verification gap by using Psyche's Controls Analysis System Testbed/GNC Integrated Systems Testbed (CAST/GIST) tool to conduct nonlinear simulations. Our results show that the gain margins for the CGS controller of the nonlinear system are within 0.3 dB of the linear values, while those for the RWA controller are within 1 dB. In both cases, the nonlinear results show wider margins than those predicted by the linear analysis, confirming the robustness of the spacecraft's attitude control system. These results provide the first validation of Psyche's stability margins in the nonlinear domain.