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Abstract Islands are ideal mesocosms for studying dispersal, speciation, and extinction, but our understanding of insular radiations has long been limited by the difficulty of estimating the timing and tempo of island evolution in the absence of fossils and methods that explicitly account for the role of paleogeography in diversification. We introduce a new generalizable model, TimeFIG, which jointly infers paleogeographically-informed biogeographic rates, ancestral species ranges, and divergence times without using fossils. Using TimeFIG, we reconstruct the phylogeny of Hawaiian Kadua, an ecomorphologically diverse but understudied plant lineage in the coffee family (Rubiaceae), and estimate dispersal, speciation, and extinction rates simultaneously with divergence times and ancestral ranges. Our results support a range of colonization times, either corresponding with the rise of the oldest modern island, Kaua’i, or with older now-eroded, northwestern islands. We detect strong effects of island isolation on dispersal rates, and find highest diversification rates when islands are “middle-aged” (i.e., Goldilocks effect). Our unified spatiotemporal framework unlocks new possibilities for historical biogeography, enabling rigorous tests of foundational hypotheses in island biology and evolutionary theory.