Stable latexes containing unimolecular amphiphilic core-shell star-block polymers with a triphenylphosphine(TPP)-functionalized hydrophobic core and an outer hydrophilic shell based on anionic styrenesulfonate monomers have been synthesized in a convergent three-step strategy by reversible addition-fragmentation chain-transfer (RAFT) polymerization, loaded with [RhCl(COD)]2 and applied to the aqueous biphasic hydrogenation of styrene. When the outer shell contains sodium styrenesulfonate homopolymer blocks, treatment with a toluene solution of [RhCl(COD)]2 led to undesired polymer coagulation. Investigation of the interactions of [RhCl(COD)]2 and [RhCl(COD)(PPh3)] with smaller structural models of the polymer shell functions, namely sodium p-toluenesulfonate, sodium styrenesulfonate, and a poly(sodium styrenesulfonate) homopolymer in a biphasic toluene/water medium points to the presence of equilibrated Rh-sulfonate interactions as the cause of coagulation by inter-particle cross-linking. Modification of the hydrophilic shell to a statistical copolymer of sodium styrenesulfonate and poly(ethylene oxide) methyl ether methacrylate (PEOMA) in a 20:80 ratio allowed particle loading with the generation of core-anchored [RhCl(COD)TPP] complexes. These Rh-loaded latexes efficiently catalyze the aqueous biphasic hydrogenation of neat styrene as a benchmark reaction. The catalytic phase could be recovered and recycled, although the performances in terms of catalyst leaching and activity evolution during recycles are inferior to those of equivalent nanoreactors based on neutral or polycationic outer shells.