Several scenarios exist for the protein crystallization and aggregation in solutions near a metastable fluid-fluid phase separation below the solubility line. Based on computations, it was proposed that the fluid-fluid critical point enhances the crystallization rate by many orders of magnitude, while, based on experiments, it was proposed that the fluid-fluid spinodal controls the crystallization rate. Using molecular dynamic simulations for an isotropic model with sticky interaction, we show that neither of these scenarios adequately describes the crystallization mechanism near a metastable fluid-fluid phase separation. We find that the emergence of the high-density fluid inside the spinodal drastically enhances the crystal nucleation in the subcritical region following Ostwald's rule of stages.