Hydrodynamic interactions play a role in synchronized motions of coupled oscillators in fluids, and understanding the mechanism will facilitate development of applications in fluid mechanics. For example, synchronization phenomenon in two-phase flow will benefit the design of future microfluidic devices, allowing spatiotemporal control of microdroplet generation without additional integration of control elements. In this work, utilizing a characteristic oscillation of adjacent interfaces between two immiscible fluids in a microfluidic platform, we discover that the system can act as a coupled oscillator, notably showing spontaneous in-phase synchronization of droplet breakup. With this observation of in-phase synchronization, the coupled droplet generator exhibits a complete set of modes of coupled oscillators, including out-of-phase synchronization and nonsynchronous modes. We present a theoretical model to elucidate how a negative feedback mechanism, tied to the distance between the interfaces, induces the in-phase synchronization. We also identify the criterion for the transition from in-phase to out-of-phase oscillations.