Spectral lines formed at lower atmospheric layers show peculiar profiles at the “leading edge” of ribbons during solar flares. In particular, increased absorption of the BBSO/GST He i λ10830 line, as well as broad and centrally reversed profiles in the spectra of the Mg ii and C ii lines observed by the IRIS satellite, has been reported. In this work, we aim to understand the physical origin of such peculiar IRIS profiles, which seem to be common of many, if not all, flares. To achieve this, we quantify the spectral properties of the IRIS Mg ii profiles at the ribbon leading edge during four large flares and perform a detailed comparison with a grid of radiative hydrodynamic models using the RADYN+FP code. We also studied their transition region (TR) counterparts, finding that these ribbon front locations are regions where TR emission and chromospheric evaporation are considerably weaker compared to other parts of the ribbons. Based on our comparison between the IRIS observations and modeling, our interpretation is that there are different heating regimes at play in the leading edge and the main bright part of the ribbons. More specifically, we suggest that bombardment of the chromosphere by more gradual and modest nonthermal electron energy fluxes can qualitatively explain the IRIS observations at the ribbon leading front, while stronger and more impulsive energy fluxes are required to drive chromospheric evaporation and more intense TR emission in the bright ribbon. Our results provide a possible physical origin for the peculiar behavior of the IRIS chromospheric lines in the ribbon leading edge and new constraints for the flare models.