We introduce a generalized form of gelation theory that incorporates individual heterogeneity and show that it can explain the asynchronous, sudden appearance and growth of online extremist groups supporting ISIS (so-called Islamic State) that emerged globally post-2014. The theory predicts how heterogeneity impacts their onset times and growth profiles and suggests that online extremist groups present a broad distribution of heterogeneity-dependent aggregation mechanisms centered around homophily. The good agreement between the theory and empirical data suggests that existing strategies aiming to defeat online extremism under the assumption that it is driven by a few "bad apples" are misguided. More generally, this generalized theory should apply to a range of real-world systems featuring aggregation among heterogeneous objects.