It applies the modifier on a copy, carries the shape keys across, and then measures the result: each shape key is raised to full strength in turn and the evaluated surface is compared with the surface recorded before. The verdict is a number — how many shape keys passed and how far the worst one moved, in millimetres against the tolerance you set.

If the modifier refuses, if the vertex counts disagree, or if a shape moves past your tolerance, your mesh, your shape keys and your modifier stack are left exactly as they were, and the shape key that could not be proven is named. Modifiers that decide from the geometry, such as Decimate, can lose shapes while the vertex count and the number of keys stay identical — that is the case this add-on exists for.