In this article we study the stress time series caused by plastic avalanches in athermally sheared disordered materials. Using extensive simulations of a bidisperse Lennard-Jones system and a corresponding mesoscopic elasto-plastic model, we find that critical exponents differ from mean-field predictions, that we approach only further away from the yielding point at larger driving rates. We analyze the avalanche duration and size distributions introducing a scaling to account for the rate dependency of the dynamics. The average temporal shape of the stress drops also depends strongly on the imposed shear rate and system size. When individual avalanches are considered, they show a clear asymmetry.