Temperature-dependent onset of apparent anharmonicity in the microscopic dynamics of hydrated proteins and other biomolecules has been known as protein dynamical transition for the last quarter of a century. Using neutron scattering and molecular dynamics simulation, techniques most often associated with protein dynamical transition studies, we have investigated the microscopic dynamics of one of the most common polymers, polystyrene, which was exposed to toluene vapor, mimicking the process of protein hydration from water vapor. Polystyrene with adsorbed toluene is an example of a solvent-solute system, which, unlike biopolymers, is anhydrous and lacks hydrogen bonding. Nevertheless, it exhibits the essential traits of the dynamical transition in biomolecules, such as a specific dependence of the microscopic dynamics of both solvent and host on the temperature and the amount of solvent adsorbed. We conclude that the protein dynamical transition is a manifestation of a universal solvent-solute dynamical relationship, which is not specific to either biomolecules as solute, or aqueous media as solvent, or even a particular type of interactions between solvent and solute.