The high-redshift intergalactic medium (IGM) and the primeval galaxy population are rapidly becoming the new frontier of extra-galactic astronomy. We investigate the IGM properties and their connection to galaxies at z ≥ 5.5 under different assumptions for the ionizing photon escape and the nature of dark matter, employing our novel thesan radiation-hydrodynamical simulation suite, designed to provide a comprehensive picture of the emergence of galaxies in a full reionization context. Our simulations have realistic 'late' reionization histories, match available constraints on global IGM properties and reproduce the recently-observed rapid evolution of the mean free path of ionizing photons. We additionally examine high-z Lyman-α transmission. The optical depth evolution is consistent with data, and its distribution suggests an even-later reionization than simulated, although with a strong sensitivity to the source model. We show that the effects of these two unknowns can be disentangled by characterising the spectral shape and separation of Lyman-α transmission regions, opening up the possibility to observationally constrain both. For the first time in simulations, thesan reproduces the modulation of the Lyman-α flux as a function of galaxy distance, demonstrating the power of coupling a realistic galaxy formation model with proper radiation-hydrodynamics. We find this feature to be extremely sensitive on the timing of reionization, while being relatively insensitive to the source model. Overall, thesan produces a realistic IGM and galaxy population, providing a robust framework for future analysis of the high-z Universe.