Spatial confinement of electronic excitations in semiconductor nanocrystals (NCs) results in a significant enhancement of nonradiative Auger recombination (AR), such that AR processes can easily dominate the decay of multiexcitons. AR is especially detrimental to lasing applications of NCs, as optical gain in these structures explicitly relies on emission from multiexciton states. In standard NCs, AR rates scale linearly with inverse NC volume. Here, we investigate multiexciton dynamics in hetero-NCs composed of CdSe cores and CdS shells of tunable thickness. We observe a dramatic decrease in the AR rates at the initial stage of shell growth, which cannot be explained by traditional volume scaling alone. Rather, fluorescence-line-narrowing studies indicate that the suppression of AR correlates with the formation of an alloy layer at the core-shell interface suggesting that this effect derives primarily from the "smoothing" of the confinement potential associated with interfacial alloying. These data highlight the importance of NC interfacial structure in the AR process and provide general guidelines for the development of new nanostructures with suppressed AR for future lasing applications.