Swapping of an oxygen atom of water with that of a pentavalent actinide dioxide cation, AnO₂⁺ also called an "actinyl", requires activation of an An-O bond. It was previously found that such oxo exchange in the gas phase occurs for the first two actinyls, PaO₂⁺ and UO₂⁺, but not the next two, NpO₂⁺ and PuO₂⁺. The An-O bond dissociation energies (BDEs) decrease from PaO₂⁺ to PuO₂⁺, such that the observation of a parallel decrease in the An-O bond reactivity is intriguing. To elucidate oxo exchange, we here extend experimental studies to AmO₂⁺, americyl(V), and CmO₂⁺, curyl(V), which were produced in remarkable abundance by electrospray ionization of Am³⁺ and Cm³⁺ solutions. Like other AnO₂⁺, americyl(V) and curyl(V) adsorb up to four H₂O molecules to form tetrahydrates AnO₂(H₂O)₄⁺ with the actinide hexacoordinated by oxygen atoms. It was found that AmO₂⁺ does not oxo-exchange, whereas CmO₂⁺ does, establishing a "turn" to increasing the reactivity from americyl to curyl, which validates computational predictions. Because oxo exchange occurs via conversion of an actinyl(V) hydrate, AnO₂(H₂O)⁺, to an actinide(V) hydroxide, AnO(OH)₂⁺, it reflects the propensity for actinyl(V) hydrolysis: PaO₂⁺ hydrolyzes and oxo-exchanges most easily, despite the fact that it has the highest BDE of all AnO₂⁺. A reexamination of the computational results for actinyl(V) oxo exchange reveals distinctive properties and chemistry of curyl(V) species, particularly CmO(OH)₂⁺.