Semiconductor quantum dot/rod/emitter upconverter nanostructures are promising for photovoltaic applications due to their broadband absorption and tunability. However, the best reported upconversion quantum yield is only 2%, limited by competing carrier relaxation mechanisms. In this work, both steady-state and excitation wavelength-dependent time-resolved photoluminescence are used to measure carrier separation and transfer dynamics as a function of nanostructure morphology. We synthesize and measure core-only, core/rod intermediates, and full core/rod/emitter structures and perform three-dimensional (3D) modeling of the electron and hole wavefunctions for each of these structures. We observe that addition of the rod to the core quantum dot improves passivation and carrier separation. An increase in core homogeneity and rod alloying are both found to result in higher radiative recombination rates relative to nonradiative recombination, in agreement with an increase in upconversion efficiency, as previously reported by the authors. Collectively, these results illustrate how the nanostructure morphology and composition influence carrier separation and recombination, suggesting a path toward improved upconversion performance.