As I recall, I believe it's an induction annealing process. Standing upright, the cases pass between a set of heating elements "aimed" at the neck area of the cases. The trip takes only a few seconds, but it's enough. Annealing is a combination of both time and temperature, and there's a very specific range of hardness and ductility that has to be achieved for the finished product to come out right. The typical discoloration is the result of that brief passage.
A word of clarification is in order here; we're not the only ones who anneal our production brass. ALL manufacturers (that I'm aware of, anyway) do the same thing, including military operations like Lake City. It's a virtual necessity, considering how much work hardening occurs when the neck and shoulders are formed on most bottle necked cases. Most go ahead and polish this discoloration out before selling he cases. The military doesn't because sales appeal makes absolutely no difference to them, and we don't because customers seem to like it. Either way, if it's a bottle necked case, it got annealed at some point.
The visual appearance can be duplicated, but it doesn't necessarily mean the annealing was done correctly. For that, you need to go to something like the tempil sticks, or some other means of measuring the actual temp transferred to the brass. Start with highly polished and very clean brass if you want to duplicate that appearance, but I'd say priorities are better directed at making sure the temp is right, regardless of the look. So no, no secret to the process, and it's pretty much the industry norm.