We investigate multi-color spontaneous emission from quantum-dot- quantum-well heteronanocrystals made of onion-like (CdSe)ZnS/CdSe/ZnS (core)shell/shell/shell structures, with our theoretical results explaining experimental measurements for the first time. In such multi-layered heteronanocrystals, we discover that the carrier localization is tuned from type-1-like to type-2-like localization by controlling CdSe and ZnS shell thicknesses, and that 3-monolayer ZnS barriers are not necessarily sufficient for carrier localization, unlike in conventional (CdSe)ZnS (core)shell structures. We demonstrate that exciton localization in distinct layers of (CdSe)ZnS/CdSe/ZnS heteronanocrystals with high transition probability (for n=1 states in CdSe core and n=2 states in CdSe shell) is key to their multi-color emission.