We present 36 new 40Ar‐39Ar incremental heating age determinations from the Caribbean Large Igneous Province (CLIP) providing evidence for extended periods of volcanic activity and suggest a new tectonomagmatic model for the province's timing and construction. These new 40Ar‐39Ar ages for the Curaçao Lava Formation (CLF) and Haiti's Dumisseau Formation show evidence for active CLIP volcanism from 94 to 63 Ma. No clear changes in geochemical character are evident over this period. The CLF has trace element signatures (e.g., Zr/Nb = 10–20) and flat rare earth element (REE) trends consistent with plume volcanism. The Dumisseau Formation also has plume‐like geochemistry and steeper REE trends similar to ocean island basalts. Volcanism in the Dumisseau Formation appears to have largely ceased by 83 Ma while at Curaçao it continued until 63 Ma. A rapidly surfacing and melting plume head alone does not fit this age distribution. Instead, we propose that the residual Galapagos plume head, following initial ocean plateau construction, was advected eastward by asthenospheric flow induced by subducting oceanic lithosphere. Slab rollback at the Lesser Antilles and Central America subduction zones created an extensional regime within the Caribbean plate. Mixing of plume with upwelling asthenospheric mantle provided a source for intermittent melting and eruption through the original plateau over a ∼30 Ma period.