The dynamics of exciton recombination in an ensemble of indirect band-gap (In,Al)As/AlAs quantum dots with type-I band alignment is studied. The lifetime of confined excitons which are indirect in momentum-space is mainly influenced by the sharpness of the heterointerface between the (In,Al)As quantum dot and the AlAs barrier matrix. Time-resolved photoluminescence experiments and theoretical model calculations reveal a strong dependence of the exciton lifetime on the thickness of the interface diffusion layer. The lifetime of excitons with a particular optical transition energy varies because this energy is obtained for quantum dots differing in size, shape and composition. The different exciton lifetimes, which result in photoluminescence with non-exponential decay obeying a power-law function, can be described by a phenomenological distribution function G(τ ), which allows one to explain the photoluminescence decay with one fitting parameter only.