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Some oceanic volcano chains violate the predictions of the hotspot hypothesis for geographic age progressions. One mechanism invoked to explain these observations is small‐scale sublithospheric convection (SSC). In this study, we explore this concept in thermo‐chemical, 3D‐numerical models. Melting due to SSC is shown to emerge in elongated features (∼750 km) parallel to plate motion and not just at a fixed spot; therefore volcanism occurs in chains but not with hotspot‐like linear age progressions. The seafloor age at which volcanism first occurs is sensitive to mantle temperature, as higher temperatures increase the onset age of SSC because of the stabilizing influence of thicker residue from previous mid‐ocean ridge melting. Mantle viscosity controls the rate of melt production with decreasing viscosities leading to more vigorous convection and volcanism. Calculations predict many of the key observations of the Pukapuka ridges, and the volcano groups associated with the Line, Cook‐Austral, and Marshall Islands.