Be sure that you're using the right Windex, not all of the cleaners made by Windex have ammonia in it and that's what you want. The ammonia will dissolve the corrosive salts from the primers.
I like to use the hottest water that I can stand, that way it evaporates faster. Be sure to put a light coat of oil on your firearm after cleaning.
+1 on the Windex w/ ammonia!!!! Not all Windex products have it.
An old black powder shooter taught me a trick 'bout cleaning corrosive stuff out of barrels.
Take your rifle to the bathroom, along with your ammonia and cleaning rod and patches. (Some windshield washer solvents have ammonia in them, too!)
Pour some ammonia into the toilet bowl slowly, so as to not cause the bowl to empty.
Put the muzzle end of the barrel into the toilet bowl.
Put a patch onto the cleaning rod and insert down the barrel.
Draw the patch back toward the breech, drawing the ammonia up the barrel.
Push back downward a couple of times, in a pumping style.
Push the cleaning rod out of the muzzle and lift muzzle out of bowl.
Remove patch and drop in bowl.
Flush.
Repeat with clean patch(es) and clean water, rinsing bore.
Drop patch into bowl and flush.
Leave the bathroom before your wife/significant other catches you, to avoid having to clean the entire bathroom!.
Clean barrel in traditional manner.
Thanks for reading.