Ultrafast emission processes are required to further improve the coincidence time resolution (CTR) of time-of-flight PET detectors. Extensive research efforts are underway in trying to generate and detect so-called prompt photons having much faster emission dynamics than conventional scintillation. In this contribution, we provide an analysis on key aspects to better model and understand the effects of prompt photons on CTR in the presence of slower scintillation processes. As some current and promising future detectors can produce both scintillation and prompt photons, we compare standard timing estimators to a statistical lower bound dedicated for these double-population detectors. We carry out this comparison for various prompt photon emission dynamics and various amounts of time overlap between the prompt and scintillation signals. Event-by-event fluctuations on the prompt photon production and detection yield are also included in the analysis of estimators and lower bounds. We show that this feature enables a better CTR match with experimental values obtained for BGO whose timing spectrum is strongly altered by a fluctuating Cherenkov yield. Finally, we discuss the effects of the anisotropic emission of Cherenkov photons. This review of key aspects of prompt-generating detectors can help define the requirements towards ultrafast timing.