DNA is well known for its programmable structures and reactions . DNA programmability also facilitates the temporal control of chemical reactions. For example, DNA computing reactions have been demonstrated, such as the chemical oscillation of DNA concentrations , temporal logic circuit , and timing-controlled generation of chemical signals . Moreover, the programmability of DNA has been utilized not only for controlling chemical reactions but also for controlling the physical dynamics of mechanical DNA-based nanostructures . Particularly, DNA-based coacervates (also referred to as DNA droplets) formed with branched DNA nanostructures can couple physical dynamics with chemical reactions in a programmable manner. DNA droplets divide autonomously with enzymatic and photo cleavage reactions and locomotion via enzymatic degradation . Phase separation of DNA droplets based on molecular logic computation and reaction-diffusion pattern formation coupled with RNA transcription and diffusion have also been demonstrated. However, achieving the timing-controlled physical dynamics of DNA droplets coupled with non-equilibrium chemical reactions remains challenging.