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Active emulsions can spontaneously form self-propelled droplets or phoretic micropumps. It has been predicted that the interaction with their self-generated chemical fields can lead to multistable higher-order flows and chemodynamic phenomena. However, it remains unclear how such reaction-advection-diffusion instabilities can emerge from the interplay between chemical reactions and interfacial hydrodynamics. Here, we simultaneously measure the flow fields and the chemical concentration fields using dual-channel microscopy for oil droplets that dynamically solubilize in a supramicellar aqueous surfactant solution. We developed an experimentally tractable setup with micropumps, droplets that are pinned between the top and bottom surfaces of a microfluidic reservoir, which we compare directly to predictions from a Brinkman squirmer model to account for the confinement. With increasing droplet radius, we observe (i) a migration of vortex flows from the posterior to the anterior of the droplet, analogous to a transition from pusher- to puller-type swimmers, (ii) a bistability between dipolar and quadrupolar flow modes, and, eventually, (iii) a transition to multipolar modes. We also investigate how the dynamics evolve over long time periods. Together, our observations suggest that a local build-up of chemical products leads to a saturation of the surface, which controls the propulsion mechanism. These multistable dynamics can be explained by the competing time scales of slow micellar diffusion governing the chemical buildup and faster molecular diffusion powering the underlying transport mechanism. Our results are directly relevant to phoretic micropumps, but also shed light on the interfacial activity dynamics of self-propelled droplets and other active emulsion systems