CdTe/CdSe core/shell nanocrystals are the prototypical example of type-II nanoheterostructures, in which the electron and the hole wave functions are localized in different parts of the nanostructure. As the thickness of the CdSe shell increases above a few monolayers, the spectroscopic properties of such nanocrystals change dramatically, reflecting the underlying type-I → type-II transition. For example, the exciton Stokes shift and radiative lifetime increase, while the decreasing biexciton binding energy changes sign from positive to negative. Recent experimental results for CdSe nanocrystals isoelectronically doped with a few Te substitutional impurities, however, have revealed a very different dependence of the optical and electronic properties on the nanocrystal size. Here we use atomistic calculations based on the pseudopotential method for single-particle excitations and the configuration-interaction approach for many-particle excitations to investigate carrier localization and electronic properties of CdTe/CdSe nanocrystals as the size of the CdTe core decreases from a few nm (characteristic of core/shell CdTe/CdSe nanocrystals) to the single impurity limit. We find that the unusual spectroscopic properties of isoelectronically doped CdSe:Te nanocrystals can be rationalized in terms of the change in the localization volume of the electron and hole wave functions as the size of the nanocrystal increases. The size dependence of the exciton Stokes shift, exciton radiative lifetime, and biexciton binding energy reflects the extent of carrier localization around the Te impurities.