Due to the existence of spatial walk-off and/or group-velocity mismatch effects, pump-to-signal phase transfer becomes inevitable during parametric amplification. We experimentally demonstrate that in hybrid seeded optical parametric amplifiers (OPAs) that include two OPA stages seeded by the signal and idler waves, respectively, the phase of the output signal can be restored to its initial value, although there are spatial and temporal phase fluctuations on the pump source. This method significantly relaxes the requirement for high pump beam quality, which is always very stringent in parametric amplification systems. With the introduction of this scheme into birefringent phase-matching OPAs or chirped-pulse OPAs, it should be promising to achieve intense femtosecond laser pulses that are close to the diffraction limit in space and ultra-high contrast in time, simultaneously.