Optical frequency combs have revolutionized frequency metrology and spectroscopic measurements, enabling the most precise measurements of all physical quantities. However, precision frequency metrology heavily relies on mode‐locked laser combs, which are only directly available for a few selected near‐infrared wavelength ranges. Recently, a strong tendency emerged for combs in the mid‐infrared molecular fingerprint region. To this end, several methods for wavelength conversion have been proposed and demonstrated, which nevertheless cost a degradation of coherence properties. Here a first approach is presented toward measuring resulting phase noise fluctuations, exploiting the temporal resolution of the dispersive temporal interferometry (DTI) technique for experimentally unveiling the carrier‐envelope phase dynamics of a cw‐seeded femtosecond optical parametric amplifier (OPA). Particularly, it is experimentally demonstrated for the first time that unexpectedly low seed power levels suffice to exceed vacuum fluctuations by more than an order of magnitude, resulting in pulse‐to‐pulse phase fluctuations of 82 mrad at rather moderate cw seed levels of 8 mW. Additionally, a formula is provided that allows exact prediction of the experimentally observed noise levels. This study therefore provides new insight into the role of vacuum fluctuations in OPAs, which open up an avenue for coherent dual‐comb systems in the mid‐infrared and beyond.