The transition from titanium-sapphire to ytterbium-based laser technology enables turnkey implementations of high-order harmonic generation (HHG) setups at high repetition rates, opening up new applications, e.g., in semiconductor metrology. This, however, requires exploring and understanding the impact of new experimental conditions. Here, we study HHG in neon over the spectral range 8-17 nm with high spectral resolution, using a post-compressed ytterbium laser. Our measurements reveal a large pulse-energy- and pressure-dependent spectral shift, spanning more than two harmonic orders. The femto-chirp of the harmonic emission combined with the blueshift of the fundamental field allows us to relate the observed spectral shifts to the temporal window of harmonic generation, which is determined by phase-matching. To understand these dynamics, it is essential to consider the reshaping of the driving laser field inside the plasma, despite the low driving intensity and long pulse duration. We introduce an on-axis phase-matching description that captures these effects and reproduces the experimental and simulated trends. These results demonstrate the central role of plasma-induced laser reshaping in phase-matching of HHG, which should be accounted for when optimizing sources in a multi-parameter landscape.