We present a novel phase-shifting interferometry technique for investigations of the unsteady kinetics and the formation of spatio-temporal patterns during the protein crystallization. We applied this technique to the ferritin crystal growth, which is controlled by the rate of supply of material. We find strong fluctuations of growth rate, step density and step velocity due to passage of step bunches. The fluctuation amplitudes decrease with higher supersaturation and larger crystal size, as well as with increasing distance from the step sources. Since these are parameters affecting the solute supply field, we conclude that fluctuations are rooted in the coupling of the interfacial processes of growth to the bulk transport in the solution. Analysis of the step velocity dependence on local slope indicates a very weak interaction between the steps. Hence, in diffusion-controlled systems with non-interacting or weakly interacting steps the stable growth mode is that via equidistant step trains, and randomly arising step bunches decay.