Polymerization-induced self-assembly (PISA) has established itself as a powerful and straightforward method to produce polymeric nano-objects of various morphologies in (aqueous) solution. Generally, spheres are formed in the early stages of polymerization that may evolve to higher order morphologies (worms or vesicles), as the solvophobic block grows during polymerization. Hitherto, the mechanisms involved in these morphological transitions during PISA are still not well understood. Combining a systematic study of a representative PISA system with rheological measurements, we demonstrate that-unexpectedly-unimer exchange is not necessary to form higher order morphologies during radical RAFT-mediated PISA. Instead, in the investigated aqueous PISA, the monomer present in the polymerization medium is responsible for the morphological transitions, even though it slows down unimer exchange.