The general dynamic model (GDM) of oceanic island biogeography views oceanic islands predominantly as sinks rather than sources of dispersing lineages. To test this, we conducted a biogeographic analysis of a highly successful insular plant taxon, Cyrtandra, and inferred the directionality of dispersal and founder events throughout the four biogeographical units of the Indo‐Australian Archipelago (IAA), namely Sunda, Wallacea, Philippines, and Sahul. Sunda was recovered as the major source area, followed by Wallacea, a system of oceanic islands. The relatively high number of events originating from Wallacea is attributed to its central location in the IAA and its complex geological history selecting for increased dispersibility. We also tested if diversification dynamics in Cyrtandra follow predictions of adaptive radiation, which is the dominant process as per the GDM. Diversification dynamics of dispersing lineages of Cyrtandra in the Southeast Asian grade showed early bursts followed by a plateau, which is consistent with adaptive radiation. We did not detect signals of diversity‐dependent diversification, and this is attributed to Southeast Asian cyrtandras occupying various niche spaces, evident by their wide morphological range in habit and floral characters. The Pacific clade, which arrived at the immaturity phase of the Pacific Islands, showed diversification dynamics predicted by the island immaturity speciation pulse model (IISP), wherein rates increase exponentially, and their morphological range is controlled by the least action effect favoring woodiness and fleshy fruits. Our study provides a first step toward a framework for investigating diversification dynamics as predicted by the GDM in highly successful insular taxa.