We theoretically analyze the Bragg spectroscopic interferometer of two spatially separated atomic Bose-Einstein condensates that was experimentally realized by Saba et al. [Science 2005 307 p1945]. Although the relative phase evolution is continuously monitored by light-stimulated Bragg scattering of intense laser beams, we show that the phase is created by quantum measurement-induced back-action on the homodyne photo-current of the lasers,opening possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a running phase regime, that is sensitive to an energy offset and suitable for an interferometer, and a trapped phase regime, that can be insensitive to applied forces and detrimental to interferometric applications.