We consider two classes of minimally supersymmetric STU-models in four dimensions motivated by their (conjectured) origin, respectively, from reductions of massive type IIA string theory on SU(3)-structure manifolds and M-theory on G2-structure. In both cases, we identify the geometric origin of the moduli ?fields and derive the dictionary between metric fluxes and torsion classes. The matching between the expression of the Ricci scalar and the metric flux-induced scalar potential works in any point of moduli space and regardless of whether or not Jacobi constraints have been imposed on the metric flux components. Finally, we provide the ten- or eleven-dimensional uplift of the aforementioned supergravity models by showing the equivalence between higher-dimensional and four-dimensional equations of motion.