We study theoretically x-ray absorption and ionization spectra of an atom or molecule by two coherent x-ray pulses that show a relative phase shift resulting in a time delay of the pulse envelopes. We demonstrate that the phase modulation of the spectra is shifted with respect to the phase oscillation comb of the x-ray double pulse. The reason for this shift is the dynamics of the process defined by the interplay of the delay time, the pulse width, the detuning, and the lifetime of the core-excited state.