Complex fluids subjected to localized microscopic energy inputs exhibit nonequilibrium behaviors that are poorly understood. For the case of a laser-trapped probe dragged at a mean constant speed, we introduce a general method grounded in the breakdown of the equipartition theorem to identify changes in the fluid’s microstructural conformation. Specifically, we have linked the different scaling regimes in the probe’s position variance, obtained through large-scale Brownian simulations of polymers, to a transition from diffusive to jump dynamics, where the fluid intermittently relaxes accumulated stress. Furthermore, our numerical findings, supported by effective analytic modeling, provide insights into the probe’s frictional response. Our method overcomes the limitations of continuum macroscopic descriptions of the fluid, which break down when the driving length scale approaches the characteristic size of fluid constituents.