We have investigated the charge transfer mechanism in single crystals of DTBDT-TCNQ and DTBDT-F4TCNQ (where DTBDT is dithieno[2,3-d;2',3'-d'] benzo[1,2-b;4,5-b']dithiophene) using a combination of near-edge X-ray absorption spectroscopy (NEXAFS) and density functional theory calculations (DFT) including final state effects beyond the sudden state approximation. In particular, we find that a description that considers the partial screening of the electron-hole Coulomb correlation on a static level as well as the rearrangement of electronic density shows excellent agreement with experiment and allows to uncover the details of the charge transfer mechanism in DTBDT-TCNQ and DTBDT-F4 TCNQ, as well as a reinterpretation of previous NEXAFS data on pure TCNQ. Finally, we further show that almost the same quality of agreement between theoretical results and experiment is obtained by the much faster Z+1/2 approximation, where the core hole effects are simulated by replacing N or F with atomic number Z with the neighboring atom with atomic number Z+1/2.