We extend the FONLL general-mass variableflavour-number scheme to the case of longitudinally polarised DIS structure functions, accounting for perturbative corrections up to O α2 s . We quantify the impact of charm quark mass and higher-order perturbative corrections on projected measurements of inclusive and charm-tagged longitudinal asymmetries at the Electron-Ion Collider (EIC) and at the Electron-ion collider in China (EicC). We demonstrate how the inclusion of these corrections is essential to compute predictions with an accuracy that matches the projected precision of the measurements. The computation is made publicly available through the open-source EKO and YADISM programs.