It was recently shown that the kinetics of persistent photoconductivity (PPC) build-up in indium doped Cd(1-x)Mn(x)Te are non-exponential and can be described solely by the stretched-exponential function. The non-exponentiality is attributed to the indium related DX centers present in the materials. In order to explain this observation, low temperature photoconductivity build-up was studied for Cd(1-x)Mn(x)Te:In of two different manganese contents. It was found that this type of response has its origin in the heavy-tailed distribution of the DX centers. The distribution was analyzed in terms of photon flux. Increasing photon flux leads to the more dispersive behavior. It was also confirmed that the heavy-tailed distribution is due to the different local configuration of atoms surrounding DX centers in the alloy.