ZnS shelling of I-III-VI nanocrystals (NCs) invariably leads to blue-shifts in both the absorption and photoluminescence spectra. These observations imply that the outcome of ZnS shelling reactions on I-III-VI colloidal NCs results from a complex interplay between several processes taking place in solution, at the surface of, and within the seed NC. However, a fundamental understanding of the factors determining the balance between these different processes is still lacking. In this work, we address this need by investigating the impact of precursor reactivity, reaction temperature, and surface chemistry (due to the washing procedure) on the outcome of ZnS shelling reactions on CuInS NCs using a seeded growth approach. We demonstrate that low reaction temperatures (150 °C) favor etching, cation exchange, and alloying regardless of the precursors used. Heteroepitaxial shell overgrowth becomes the dominant process only if reactive S- and Zn-precursors (S-ODE/OLAM and ZnI) and high reaction temperatures (210 °C) are used, although a certain degree of heterointerfacial alloying still occurs. Remarkably, the presence of residual acetate at the surface of CIS seed NCs washed with ethanol is shown to facilitate heteroepitaxial shell overgrowth, yielding for the first time CIS/ZnS core/shell NCs displaying red-shifted absorption spectra, in agreement with the spectral shifts expected for a type-I band alignment. The insights provided by this work pave the way toward the design of improved synthesis strategies to CIS/ZnS core/shell and alloy NCs with tailored elemental distribution profiles, allowing precise tuning of the optoelectronic properties of the resulting materials.