Long-lived oscillations in 2D spectra of chlorophylls are at the heart of an ongoing debate. Their physical origin is either a multipigment effect, such as excitonic coherence, or localized vibrations. We show how relative phase differences of diagonal- and cross-peak oscillations can distinguish between electronic and vibrational (vibronic) effects. While direct discrimination between the two scenarios is obscured when peaks overlap, their sensitivity to temperature provides a stronger argument. We show that vibrational (vibronic) oscillations change relative phase with temperature, while electronic oscillations are only weakly dependent. This highlights that studies of relative phase difference as a function of temperature provide a clear and easily accessible method to distinguish between vibrational and electronic coherences.