This study used direct numerical simulations (DNSs) of combustion processes in turbulent heterogeneous mixtures for self-igniting partially-premixed configurations to assess the accuracy of partially-premixed turbulent combustion models that are based on the tabulation of chemistry progress in homogeneous reactors (HRs). DNS coupled with n-heptane/air detailed chemistry solving was considered as a reference result. Because the same detailed chemistry was used to generate the chemistry databases, the study was focused entirely on validating the modelling assumptions. Various HR-based tabulation models were tested: (1) the tabulated homogeneous reactor (THR) model, which is a direct exploitation of HR tabulation lacking any statistical information concerning mixture heterogeneity; (2) the presumed conditional moment (PCM) model, which includes a limited statistical description of the mixture and/or of the combustion advancement; (3) approximated diffusion flame (ADF) models, which consider the heterogeneous turbulent reactor as either a unique diffusion flame (simple ADF model formulation) or as a collection of flamelets with different strain rates (ADFχ model). A priori response of the above mentioned models was compared with detailed chemistry DNS results. The main findings are as follows: (1) A direct use of HR tabulation (THR model) led to overly inaccurate results; (2) an assumed independence between mixture fraction and progress variable was responsible for most PCM modelling failures in the context of turbulent heterogeneous self-ignited combustion; (3) the presumed beta-function of the progress variable distribution is likely to fail because of the complexity of auto-ignition kinetics; (4) the best results were obtained with the ADF models; (5) a simple ADF formulation is preferable to ADFχ, which showed limitations in terms of accuracy concerning the distribution of the progress variable ;(6) all tested models provided an acceptable prediction of the auto ignition delays but only ADF and ADFχ models are able to represent the temporal evolution of the progress variable.