I don't have any idea why copper sulfate is in many of the old formulas. Maybe in conjunction with some of the other chemicals it helps promote the rusting. I don't believe that in itself it does that to the steel.
I've read that some of the old formulas have un-necessary chemicals in them or one that will cancel out another. With the long list that is in some I can believe it, but again ,,not a chemistry major here.

I did read somewhere ( a John Bivins M/L article I believe) that the developer of Laurel Mtn Soln, Rick Schreiber (sp?), put a small amt of copper sulfate in the L/Mtn originally as a marker of sorts.
As the coating quickly dries, especially on the first couple of coats on fresh steel, the dark blue/gray color is easy to see where you've been,,or not.
Personally, I could do w/o it being in there if that's all it's for. Every once in a while I still get a small copper plated area from over lapping a few strokes of the swab. Otherwise it's Ferric Chloride as the rusting agent AFAIK and that makes a first rate slow rust solution.

If the bbls are too warm,,it will 'plate out' in bright copper onto the steel.
Much the same way as any of the old mercury (bichloride) rust blue compounds will plate out the bright mercury but only onto brass, copper, gold, ect inlays in the warm steel for you.

Very stubborn stuff to remove, the mercury is. All your gold inlay work will look nickle plated if you use the wrong soln.
Shouldn't be any reason for using that merc stuff anymore anyway..