The activation of carbon dioxide (CO2) by a transition-metal cation in the gas phase is a unique model system for understanding single-atom catalysis. The mechanism of such reactions is often attributed to a "two-state reactivity" model in which the high-energy barrier of a spin state correlating with ground-state reactants is avoided by intersystem crossing (ISC) to a different spin state with a lower barrier. However, such a "spin-forbidden" mechanism, along with the corresponding dynamics, has seldom been rigorously examined theoretically, due to the lack of global potential energy surfaces (PESs). In this work, we report full-dimensional PESs of the lowest-lying quintet, triplet, and singlet states of the TaCO2+ system, machine-learned from first-principles data. These PESs and the corresponding spin-orbit couplings enable us to provide an extensive theoretical characterization of the dynamics and kinetics of the reaction between the tantalum cation (Ta+) and CO2, which have recently been investigated experimentally at high collision energies using crossed beams and velocity map imaging, as well as at thermal energies using a selected-ion flow tube apparatus. The multistate quasi-classical trajectory simulations with surface hopping reproduce most of the measured product translational and angular distributions, shedding valuable light on the nonadiabatic reaction dynamics. The calculated rate coefficients from 200 to 600 K are also in good agreement with the latest experimental measurements. More importantly, these calculations revealed that the reaction is controlled by intersystem crossing, rather than potential barriers.