Using three-dimensional hydrodynamical simulations of isolated dwarf spheroidal galaxies (dSphs), we undertake an analysis of the chemical properties of their inner regions, identifying the respective roles played by Type Ia supernovae (SNe Ia) and Type II supernovae (SNe II). The effect of inhomogeneous pollution from SNe Ia is shown to be prominent within two core radii, with the stars forming therein amounting to ~20 per cent of the total. These stars are relatively iron-rich and α-element depleted compared to the stars forming in the rest of the galaxy. At odds with the projected stellar velocity dispersion radial profile, the actual three-dimensional one shows a depression in the central region, where the most metal-rich (i.e. [Fe/H]-rich) stars are partly segregated. This naturally results in two different stellar populations, with an anticorrelation between [Fe/H] and velocity dispersion, in the same sense as that observed in the Sculptor and Fornax dSphs. Because the most iron-rich stars in our model are also the most α depleted, a natural prediction and test of our model is that the same radial segregation effects should exist between [α/Fe] and velocity dispersion.