The demand for computational tools that are capable to reliably predict the behavior of a nuclear reactor core in a variety of static and dynamic conditions does inevitably require a proper qualification of these tools for the intended purposes. One of the qualification methods is the verification of the code in question. Hereby, the correct implementation of the applied model as well as its flawless implementation in the code are scrutinized. The present work concerns with benchmarking as a substantial part of the verification of the three-dimensional, multigroup neutron kinetics model employed in the transient code POLCA-T. The benchmarking is done by solving some specified and widely used space-time kinetics benchmark problems and comparing the results to those of other, established and well-proven spatial kinetics codes. It is shown that the obtained results are accurate and consistent with corresponding solutions of other codes. In addition, a sensitivity analysis is carried out with the objective to study the sensitivity of the POLCA-T neutronics to variations in different numerical options. It is demonstrated that the model is numerically stable and provide reproducible results for a wide range of various numerical settings. Thus, the model is shown to be rather insensitive to significant variations in input, for example. The other consequence of this analysis is that, depending on the treated transient, the computing costs can be reduced by, for instance, employing larger time-steps during the time-integration process or using a reduced number of iterations. Based on the outcome of this study, one can finally conclude that the POLCA-T neutron kinetics is modeled and implemented correctly and thus, the model is fully capable to perform the assigned tasks.