The Hawaiian silversword alliance (Asteraceae) is an iconic adaptive radiation. However, like many island plant lineages, no fossils have been assigned to the clade. As a result, the clade's age and diversification rate are not known precisely, making it difficult to test biogeographic hypotheses about the radiation. Without fossils, paleogeographically structured biogeographic processes may inform species divergence times; for example, an island must first exist for a clade to radiate upon it. We date the silversword clade and test biogeographic hypotheses about its radiation across the Hawaiian Archipelago by modeling interactions between species relationships, molecular evolution, biogeographic scenarios, divergence times, and island origination times using the Bayesian phylogenetic framework, RevBayes. The ancestor of living silverswords most likely colonized the modern Hawaiian Islands once from the mainland approximately 5.1 Ma, with the most recent common ancestor of extant silversword lineages first appearing approximately 3.5 Ma. Applying an event-based test of the progression rule of island biogeography, we found strong evidence that the dispersal process prefers old-to-young directionality, but strong evidence for diversification continuing unabated into later phases of island ontogeny, particularly for Kauai. This work serves as a general example for how diversification studies benefit from incorporating biogeographic and paleogeographic components.