Self-assembled Cd(Se,Te) quantum dots with various Se compositions embedded in the ZnTe matrix are grown by molecular beam epitaxy. A huge redshift of the near band edge emission, from 2.1 eV to 1.5 eV, with an increasing Se content in the dots is observed. It is accompanied by an increase in the excitonic lifetime by the factor of 10. We associate these effects with a gradual change from the direct type I confinement character in CdTe/ZnTe quantum dots to the staggered type II band alignment in the case of Cd(Se,Te)/ZnTe dots. This interpretation is consistent with the micro-photoluminescence study of several individual quantum dots, which reveals a gradual decrease in the biexciton–exciton energy difference with the increasing content of Se in the dots, which leads ultimately to the change from the binding to antibinding character of biexcitons. The latter effect originates, most likely, from the increasing Coulomb repulsion between excitons forming dipoles at the dot/barrier interface.