Excitons, quasi-particles generated by the Coulomb interaction between an excited electron and a hole, have been proposed as a possibility to overcome the limits of electronics. To fully exploit them, a deeper understanding of their interaction with light is required. In this study, the interaction of a core exciton with an intense, few-femtosecond infrared pulse is investigated with attosecond transient reflection spectroscopy in a bulk monocrystalline MgF2 sample. The distinct few- and sub-femtosecond optical responses attest the dual, atomic- and solid-like, nature of core excitons. Sub-femtosecond dynamics, in particular, are dictated by the interplay between the exciton and the conduction band of the crystal. Theoretical simulations allow to propose the exciton binding energy as a lever to control exciton dynamics on an ultrafast timescale.