We study the liquid-liquid phase separation (LLPS) of a cell-free transcription-translation (TXTL) system. When the TXTL reaction, composed of a large amount of proteins, is concentrated, the uniformly mixed state becomes unstable and membrane-less droplets form spontaneously. This LLPS droplet formation can be induced when the TXTL reaction is enclosed in water-in-oil emulsion droplets in which water evaporates (dehydration) from the surface. As the emulsion droplets shrink, smaller LLPS droplets appear inside the emulsion droplets and coalesce into phase-separated domains that partition the location of proteins. We show that the LLPS in the emulsion droplets can be accelerated by interfacial drift in the outer oil phase. This further provides an experimental platform for studying the interplay between biological reactions and intracellular phase separation.