Zn_xCd_1-xSe/C core/shell nanocrystals with 31-39 nm semiconducting core and 11-25 nm carbon shell were synthesized from solid state precursors in large scale amounts. Rietveld analysis of the X-ray diffraction patterns of the samples prepared in three different ways, all under their autogenic pressure, reveal varying compositions of the Zn_xCd_1-xSe nanocrystal core, where the cubic phases with higher Zn content were dominant compared to the hexagonal phases. Transmission electron microscopy (TEM) showed striations in the nanocrystals that are indicative of a composition modulation, and reveal a chemical phase separation and spinodal decomposition within the nanocrystals. The optical properties and carrier relaxation kinetics of the nanocrystals were examined with time-resolved cathodoluminescence (CL). We observed that groups of nanocrystals within regions of constant wavelength exhibit very similar local CL spectra, in which the highly focused electron beam remains fixed on a localized region, during the acquisition of a CL spectrum. The CL spectral lineshape was found to depend on the excitation level, temperature, and time-window during time-delayed spectroscopy. Time-delayed CL spectroscopy at different temperatures was used to construct snap shots of the spectral lineshape during the decay. Variations in the lineshape with temperature were found to be consistent with the carrier transport and thermalization between the phase-separated Cd-rich regions and the homogenous Zn0_.47Cd_0.53Se alloy regions in the nanocrystals. A 2D band-filling model was used to examine the carrier filling in Cd-rich regions as a function of e-beam current, as based on the excitation dependence of emission from the Cd-rich regions and the homogenous Zn0_.47Cd_0.53Se alloy regions. These results illustrate that compositional phase separation on the scale of ~1-5 nm in II-VI nanocrystals can lead to potentially useful quantum effects and interesting optical properties.