Gravitational-wave data from interferometric detectors like LIGO, Virgo and KAGRA is routinely analyzed by rapid matched-filtering algorithms to detect compact binary merger events and rapidly infer their spatial position, which enables the discovery of associated non-GW transients like GRB 170817A and AT2017gfo. One of the critical requirements for finding such counterparts is that the rapidly inferred sky location, usually performed by the Bayestar algorithm, is correct. The reliability of this data product relies on various assumptions and a tuning parameter in Bayestar, which we investigate in this paper in the context of PyCBC Live, one of the rapid search algorithms used by LIGO, Virgo and KAGRA. We perform simulations of compact binary coalescence signals recovered by PyCBC Live and localized by Bayestar, under various configurations with different balances between simplicity and realism, and we test the resulting sky localizations for consistency based on the widely-used PP plot. We identify some aspects of the search configuration which drive the optimal setting of Bayestar's tuning parameter, in particular the properties of the template bank used for matched filtering. On the other hand, we find that this parameter does not depend strongly on the nonstationary and non-Gaussian properties of the detector noise.