The aim of this work has been to improve the time resolution of radiation detectors for future high-energy physics experiments and medical imaging applications. Ce-doped oxyorthosilicate Lu2SiO5:Ce (LSO) and mixed oxyorthosilicate Lu1.6Y0.4SiO5:Ce (LYSO) have been investigated as prospective scintillators for such high-time-resolution applications. A differential optical absorption technique with sub-picosecond time resolution upon selective excitation of Ce3+ ions to different excited states has been adopted to study carrier dynamics in these scintillators, and coincidence time resolution measured using 511 keV γ-quanta has been exploited to test their timing properties. A delay in population of the emitting level of Ce3+ has been observed, and is interpreted in terms of electron trapping, which is more pronounced in mixed yttrium-containing LYSO crystals due to composition fluctuations. It is shown that the delay, which affects the luminescence response time, can be eliminated by co-doping of LYSO:Ce with calcium at concentrations as low as 5 ppm. The faster kinetics of electron transfer correlates with a better coincidence time resolution. Thermalization and spatial distribution of non-equilibrium carriers has been studied theoretically to link the results obtained by the time-resolved differential optical absorption technique with the behavior of the non-equilibrium carriers generated by irradiation.