The anisotropy of the Zeeman splitting of bound excitons is studied as a function of the magnetic field direction in CdTe films doped with different dopants. The observed internal distortion is associated with defect complexes consisting of n-type dopants chlorine, iodine and indium compensated by nearby Cd vacancies. The Zeeman splittings observed in luminescence experiments at low temperatures are discussed in terms of a modified Hamiltonian taking into consideration the reduced site symmetry of the traps. The corresponding g-factor of the electron, the hole parameters K and L and an additional distortion parameter ratio W/D have been determined for the prominent A-, A'- and C-line. The diamagnetic shifts are discussed revealing the reduced mass of the bound excitons. After several months of storage at room temperature distinct changes of the photoluminescence are observed indicating that formation of defects takes place with time. Proposed microscopic models are discussed and compared with our experimental findings.