Two improvements to the binary structural phase field crystal (XPFC) theory are presented. The first is an improvement to the phenomenology for modelling density-density correlation functions and the second extends the free energy of the mixing term in the binary XPFC model beyond ideal mixing to a regular solution model. These improvements are applied to study kinetics of precipitation from solution. We observe a two-step nucleation pathway similar to recent experimental work [N. D. Loh, S. Sen, M. Bosman, S. F. Tan, J. Zhong, C. A. Nijhuis, P. Král, P. Matsudaira, and U. Mirsaidov, Nat. Chem. 9, 77 (2017)10.1038/nchem.2618; A. F. Wallace, L. O. Hedges, A. Fernandez-Martinez, P. Raiteri, J. D. Gale, G. A. Waychunas, S. Whitelam, J. F. Banfield, and J. J. De Yoreo, Science 341, 885 (2013)SCIEAS0036-807510.1126/science.1230915] in which the liquid solution first decomposes into solute-poor and solute-rich regions, followed by precipitate nucleation of the solute-rich regions. Additionally, we find a phenomenon not previously described in the literature in which the growth of precipitates is accelerated in the presence of uncrystallized solute-rich liquid regions.