Athermal, disordered solids deform plastically via avalanches in the quasistatic limit of shear. These avalanches display critical behavior including power-law distributions. With increasing strain rate, the system moves away from the critical point causing a decrease in the correlation length of the system. We explore 2D and 3D simulations of overdamped binary Lennard-Jones solids in the limit of finite strain rate and characterize the temporal and spatial correlations that govern avalanche plasticity. With increasing strain rate, we identify a decreasing length scale in the power spectrum of the non-affine displacement of particles and a decreasing time scale in the power spectrum of temporal fluctuations in the average kinetic energy and stress. Using finite-size scaling, we find the critical exponents governing the scaling of correlations with rate. We will also relate these results to the scaling of other system properties with strain rate such as a size-dependent diffusion constant in 2D and the average shear stress.