Digestion of cellulosic biomass solids may be complicated by release of lignin therefrom. Methods for digesting cellulosic biomass solids may comprise: heating cellulosic biomass solids and a digestion solvent in the presence of molecular hydrogen and a slurry catalyst capable of activating molecular hydrogen, thereby forming a phenolics liquid phase comprising lignin, an aqueous phase comprising an alcoholic component derived from the cellulosic biomass solids, and an optional light organics phase, the slurry catalyst being distributed in the cellulosic biomass solids and at least a portion of the slurry catalyst accumulating in the phenolics liquid phase as it forms; conveying at least a portion of the phenolics liquid phase and the slurry catalyst to a location above at least a portion of the cellulosic biomass solids; and after conveying the phenolics liquid phase and the slurry catalyst, releasing them such that they come in contact with the cellulosic biomass solids.