What happens when you mix albumin protein and protease?

First, I assume you tested the protein content using a Biuret solution, not a Bituret solution.
The Biuret reaction measures the amount of peptide bonds, or in other words the concentration of proteins. Protease will cut/break proteins, so you would expect that a solution with albumin alone will give a more intense coloring than albumine + protease.

Secondly, it is hard to answer your question without seeing a graph of the protein content. Did you see a clear pattern? Maybe there is a certain salt concentration at which the enzyme works best? At very high or low salt concentrations, your protein itself might fall apart, while in the middle, the enzyme (protease) will start to work. If so, the curve that you describe might actually make sense. There might be 2 factors at work: protein degradation by high salt concentration and protein degradation in moderate salt conditions because then the enzyme starts to work.

But it is hard to explain your results without me being present and seeing the results.

But if there is a clear pattern in you