A time-domain characterization and stochastic model are developed for analyzing the evolution of the early randomization of fields inside mode-stirred reverberation chambers. The chamber is excited by a pulse amplitude modulated RF signal and stirred mechanically by a rotational stirrer. Phase noise (jitter) in the arrival times of a received pulse train is found to contain a systematic contribution that depends on stir speed and stir sense, as well as a random contribution governed by the rate of field depolarization. For the systematic component, a model of the phase delay for a uniformly orbiting scatterer inside a cavity is derived. For the random component, a nonhomogeneous Poisson model for arrivals of wave fronts in a nonstationary stir process exhibits good agreement with the empirical distribution of the measured jitter. At increasing stir velocities, the rate of field mixing increases less rapidly. The excess delay approaches asymptotically an Erlang distribution, in the limit of a homogeneous Poisson process for uniformly distributed late arrival times.