The future of nanoscale spin-based technologies hinges on a fundamental understanding and dynamic control of atomic-scale magnets. The role of the substrate conduction electrons on the dynamics of supported atomic magnets is still a question of interest lacking experimental insight. We characterized the temperature-dependent dynamical response of artificially constructed magnets, composed of a few exchange-coupled atomic spins adsorbed on a metallic substrate, to spin-polarized currents driven and read out by a magnetic scanning tunneling microscope tip. The dynamics, reflected by two-state spin noise, is quantified by a model that considers the interplay between quantum tunneling and sequential spin transitions driven by electron spin-flip processes and accounts for an observed spin-transfer torque effect.