  Understanding the dynamics of open quantum systems in strong coupling and
non-Markovian regimes remains a formidable theoretical challenge. One popular
and well-established method of approximation in these circumstances is provided
by the polaron master equation (PME). In this work we reevaluate and extend the
validity of the PME to capture the impact of non-Markovian polaron dressing,
induced by non-equilibrium open system dynamics. By comparing with numerically
exact techniques, we confirm that while the standard PME successfully predicts
the dynamics of system observables that commute with the polaron transformation
(e.g. populations in the Pauli z-basis), it can struggle to fully capture those
that do not (e.g. coherences). This limitation stems from the mixing of system
and environment degrees of freedom inherent to the polaron transformation,
which affects the accuracy of calculated expectation values within the polaron
frame. Employing the Nakajima-Zwanzig projection operator formalism, we
introduce correction terms that provide an accurate description of observables
that do not commute with the transformation. We demonstrate the significance of
the correction terms in two cases, the canonical spin-boson model and a
dissipative time-dependent Landau-Zener protocol, where they are shown to
impact the system dynamics on both short and long timescales.
