  Among expanding discoveries of quantum phases in moir\'e superlattices,
correlated insulators stand out as both the most stable and most commonly
observed. Despite the central importance of these states in moir\'e physics,
little is known about their underlying nature. Here, we use pump-probe
spectroscopy to show distinct time-domain signatures of correlated insulators
at fillings of one (v = -1) and two (v = -2) holes per moir\'e unit cell in the
angle-aligned WSe2/WS2 system. Following photo-doping, we find that the
disordering time of the v = -1 state is independent of excitation density
(n_ex), as expected from the characteristic phonon response time associated
with a polaronic state. In contrast, the disordering time of the v = -2 state
scales with (n_ex)^-0.5, in agreement with plasmonic screening from free holons
and doublons. These states display disparate reordering behavior dominated
either by first order (v = -1) or second order (v = -2) recombination,
suggesting the presence of Hubbard excitons and free carrier-like
holons/doublons, respectively. Our work delineates the roles of electron-phonon
(e-ph) versus electron-electron (e-e) interactions in correlated insulators on
the moir\'e landscape and establishes non-equilibrium responses as mechanistic
signatures for distinguishing and discovering quantum phases.
