By imposing vibration to a core-annular flow of an aqueous two-phase system (ATPS) with ultralow interfacial tension, we observe a liquid finger protruding from the interface of an expanding jet. We find that the protruded finger breaks up only when its length-to-width ratio exceeds a threshold value. The breakup follows a constant wavelength-to-width ratio that is consistent with that of breakup under Rayleigh-Plateau instability. The mechanism is applicable to aqueous two-phase systems with a large range of viscosity ratios. The protruded finger can break up into small droplets that are monodisperse in size, controllable in generation frequency under a wide range of flow rates. This work suggests a way to generate small water-water droplets with high monodispersity and production rate from a single nozzle.