It's not copper.
...color of an anodized aluminum surface.
ULA anodizes its Atlas V tank panels. That color results from the specific anodization process they use, combined with the specific aluminum alloy they use.
So, why does anodization produces this specific color? Anodization is a method to increase the thickness of the oxidized layer on a metal surface--for aluminum, that's aluminum oxide, aka corundum. Aluminum is a very soft metal, but corundum is a mineral second only to diamond in hardness. It should be apparent that the Atlas panels are anodized to increase its physical and chemical resistance to damage and wear.
The anodization process not only introduces new chemicals which could bond with the anodizing surface--my source mentions and shows sulfuric, chromic, and nitric acid used--but the process also forms microscopic holes. Perhaps those also cause light to be scattered in a specific way that produces the distinctive color? That's all I can offer--I suspect a more detailed answer is beyond the scope of this stack exchange--Chemistry is probably a good place to ask, though.
It is mentioned that the color matures as the panels sit in the atmosphere post-anodization, so that should help narrow the exact mechanism down.
Source: Tory Bruno.
(Want slightly more context? Strongly encourage you to watch the entire video.)
EDIT: In some rather coincidental timing (or perhaps a ULA employee is a Stack Exchange user?), the day after I wrote this answer, ULA tweeted the following confirmation:
"The #AtlasV stages are anodized, which is an electrochemical process that gives the metal surface a corrosion-resistant finish that is bronze in color."
EDIT #2: Tory Bruno himself dropped a juicy tidbit on Twitter today, suggesting that the unique color is caused by a coating of Tiodize applied after anodization. Thanks, Tory!