I insist on cleaning steel thoroughly prior to browning, no matter the solution. If water does not wet the steel (you can see this phenomenon by drops forming with areas of non-wet adjacent), then browning solution will not rust that area.
Following drawfiling and polishing to whatever degree the project calls for, I plug both ends of the barrel, having removed sights and breech plug, and take it to the laundry sink, where I scrub with a green Scotchbrite pad with water and Comet, a powdered cleanser. Old Dutch does not work as well. Comet is the ticket. The Comet and Scotchbrite polish the barrel a little more, and remove every vestige of oil and grease. In sight slots, I use Comet and a toothbrush, similarly around underlugs, and ribs on a half stocked barrel. Then I flush thoroughly with hot water, and check for those little islands where water doesn't wet the steel, and finding none, dry the barrel with paper towels. I move the dried barrel handling only on the plugs to the "V" blocks that will support the barrel during the browning application. My damp box has already been set up with fresh hot water and an interior light bulb for heat, and the barrel then hangs from the box's ceiling for three hours. Then I remove and apply another application of solution on the bench blocks, and then return the barrel this time the other end up, to the box. A barrel requires between five and seven of these cycles to get a good brown, here where humidity is around 30% at the best of times. If this process needs to continue the next day, because of time issues, I take the barrel out and set it in the "V" blocks overnight. Almost always, this evens out the rusting. Oh, forgot to mention; I card the barrel with a two inch diameter roll of heavy canvas, using the ends to scrub the steel, between applications. Otherwise, the barrel's surface becomes very course and grainy. Some prefer this finish, but I like the barrel's surface to be smooth, and the brown IN rather than ON the steel.
