Rigorous and intuitive master equation models are presented to study on‐demand single photon sources from pulse‐excited quantum dots coupled to optical cavities. Three methods of source excitation are considered: resonant pi‐pulse, off‐resonant phonon‐assisted inversion, and two‐photon excitation of a biexciton–exciton cascade, and the effect of the pulse excitation process on the quantum indistinguishability, efficiency, and purity of emitted photons is investigated. By explicitly modelling the time‐dependent pulsed excitation process in a manner which captures non‐Markovian effects associated with coupling to photon and phonon reservoirs, it is found that photons of near‐unity indistinguishability can be emitted with over 90% efficiency for all these schemes, with the off‐resonant schemes not necessarily requiring polarization filtering due to the frequency separation of the excitation pulse, and allowing for very high single photon purities. Furthermore, the off‐resonant methods are shown to be robust over certain parameter regimes, with less stringent requirements on the excitation pulse duration in particular. Also, a semi‐analytical simplification of the master equation is derived for the off‐resonant drive, which gives insight into the important role that exciton–phonon decoupling for a strong drive plays in the off‐resonant phonon‐assisted inversion process.