Droplets made of a water/ethanol mixture spontaneously self-propel in an oil/surfactant solution and, depending on the initial ethanol concentration at the time of production, may evolve in up to three stages. Upon self-propulsion the droplets absorb surfactant molecules during their continuous motion in the oily phase. In combination with the continuous loss of ethanol this mass exchange with the ambient phase may lead to a spontaneous phase separation of the water/ethanol mixture, and eventually to the formation of characteristic Janus droplets. Supported by experimental evidence, we propose a simple model that is able to explain the propulsion velocity and its scaling with the droplet radius in the last stage of the droplet evolution.