It is well known that performance of a thermophotovoltaic (TPV) device can be enhanced if the vacuum gap between the thermal emitter and the TPV cell becomes nanoscale due to the photon tunneling of evanescent waves. Having multiple bandgaps, multi-junction TPV cells have received attention as an alternative way to improve its performance by selectively absorbing the spectral radiation in each subcell. In this work, we comprehensively analyze the optimized near-field tandem TPV system consisting of the thin-ITO-covered tungsten emitter (at 1500 K) and GaInAsSb/InAs monolithic interconnected tandem TPV cell (at 300 K). We develop a simulation model by coupling the near-field radiation solved by fluctuational electrodynamics and the diffusion-recombination-based charge transport equations. The optimal configuration of the near-field tandem TPV system obtained by the genetic algorithm achieves the electrical power output of 8.41 W/cm$^2$ and the conversion efficiency of 35.6\% at the vacuum gap of 100 nm. We show that two resonance modes (i.e., surface plasmon polaritons supported by the ITO-vacuum interface and the confined waveguide mode in the tandem TPV cell) greatly contribute to the enhanced performance of the optimized system. We also show that the near-field tandem TPV system is superior to the single-cell-based near-field TPV system in both power output and conversion efficiency through loss analysis. Interestingly, the optimization performed with the objective function of the conversion efficiency leads to the current matching condition for the tandem TPV system regardless of the vacuum gap distances.