Heterostructuring nanocrystals into a modular metal-semiconductor configuration enables tunable and novel functionalities. Such combinations at the nanoscale equip hybrid structures with unique electronic, optical, and catalytic properties unobserved in single-phase materials. Here, we report the hot-injection synthesis of Pd-Cu3Pd13S6.65Te0.35 nanoheterostructures (NHCs) from PdCu nanoalloy seeds. First, the growth of Pd-rich chalcogenide nanocrystals was initiated over the preformed PdCu surface through simultaneous sulfidation and tellurization, followed by their transformation into Pd-Cu3Pd13S6.65Te0.35 NHCs. By strategically employing moderate-temperature annealing, we achieved the complete migration of Cu+ due to the higher reactivity of Cu in comparison to Pd at that temperature, establishing a novel mechanistic relationship between cation mobility and temperature. This strategy enables controlled semiconductor domain formation and targeted metal migration. The NHCs showed efficient and stable electrocatalytic hydrogen evolution with low Tafel values in acidic media, outperforming conventional nanoelectrocatalysts. Computational analysis identified the active sites responsible for the observed catalytic performance.