Via implicit solvent molecular dynamics simulations, we demonstrate the self-assembly of stable single and binary vesicles composed of two-tail phospholipid molecules. The amphiphilic lipid molecules are composed of a hydrophilic headgroup and two hydrophobic tails and are represented by a reduced coarse-grained model which effectively captures the key chemical and geometric attributes of phospholipid molecules. We report our measurements of the bilayer thickness to be consistent with experimental values reported in the literature. We have probed the role of temperature on the physical properties of single component lipid vesicles and found our results to concur with experimental results. Our investigations on the phase segregation in binary vesicles demonstrate that the degree of distinction between the tail groups of the lipid species can be used to tune their phase segregation in the vesicle bilayer. Finally, our measurements of the scaling exponents for macroscopically phase-segregated systems have been found to be in good agreement with theoretical and simulation studies. Our results can be used for the design of responsive biomaterials for applications in drug delivery, sensing, and imaging.