Context. The abundance of α-elements relative to iron ([α/Fe]) is an important fossil signature in Galactic archaeology for tracing the chemical evolution of disc stellar populations. High-precision chemical abundances, together with accurate stellar ages, distances, and dynamical data, are crucial to infer the Milky Way formation history. Aims: The aim of this paper is to analyse the chemodynamical properties of the Galactic disc using precise magnesium abundance estimates for solar neighbourhood stars with accurate Gaia astrometric measurements. Methods. We estimated ages and dynamical properties for 366 main sequence turn-off stars from the AMBRE Project using PARSEC isochrones together with astrometric and photometric values from Gaia DR2. We use precise global metallicities [M/H] and [Mg/Fe] abundances from a previous study in order to estimate gradients and temporal chemodynamic relations for these stars. Results: We find a radial gradient of −0.099 ± 0.031 dex kpc−1 for [M/H] and +0.023 ± 0.009 dex kpc−1 for the [Mg/Fe] abundance. The steeper [Mg/Fe] gradient than that found in the literature is a result of the improvement of the AMBRE [Mg/Fe] estimates in the metal-rich regime. In addition, we find a significant spread of stellar age at any given [Mg/Fe] value, and observe a clear correlated dispersion of the [Mg/Fe] abundance with metallicity at a given age. While for [M/H] ≤ − 0.2, a clear age–[Mg/Fe] trend is observed, more metal-rich stars display ages from 3 up to 12 Gyr, describing an almost flat trend in the [Mg/Fe]–age relation. Moreover, we report the presence of radially migrated and/or churned stars for a wide range of stellar ages, although we note the large uncertainties of the amplitude of the inferred change in orbital guiding radii. Finally, we observe the appearance of a second chemical sequence in the outer disc, 10–12 Gyr ago, populating the metal-poor, low-[Mg/Fe] tail. These stars are more metal-poor than the coexisting stellar population in the inner parts of the disc, and show lower [Mg/Fe] abundances than prior disc stars of the same metallicity, leading to a chemical discontinuity. Our data favour the rapid formation of an early disc that settled in the inner regions, followed by the accretion of external metal-poor gas –probably related to a major accretion event such as the Gaia-Enceladus/Sausage one– that may have triggered the formation of the thin disc population and steepened the abundance gradient in the early disc.