I find a coin with some toning on it now and then, but they are newer coins. An example is shown below. It's a 2001 cent! This makes me wonder how long does it normally take for a coin to start the process without being induced artificially? Does this vary depending on the content of the coin? Trying to decide how hard to wash my hands after I touch them!!!!  Anyway here is the picture. Toning is more obvious in hand.
Copper is a very reactive metal. Release a fresh new copper cent down my way with the heat, humidity and sweaty pockets, they turn in short order.
Yes the different metals tone differently. Even in the same series they will tone differently. You could have a coin tone in a summer or one that basically never does. I had a 2017 silver coin tone so wildly that people would have said it has to be induced when all it did was rest on a desk for 2 months, and other silver coins that were made 60 or so years ago that never toned. It's one of the great mysteries how some will tone quickly and others seem to never do it
And that my friends is why you eat a Krispy Kreme donut in 2 bites. And finish it off with a bag of Dixie Krystal burgers...
Coin doctors tone coins with chemicals, like sulfur. It happens very quickly. The trouble is it usually does not look natural to the experienced eye, and sometimes it keeps going. One old fashioned way is to store the coin in an envelope that is made of paper that is not sulfur free. High quality coin envelopes are made with sulfur free paper. This can work well, but it ofter takes years.
Toning begins the instant after the coin is struck, and that's on all coins, not just copper. That's because the one and only thing that's required for a coin to tone is that the coin is exposed to the air. How much and how fast any given coin tones though is always a matter of degree. It does, but it also varies depending on environment. And since environment encompasses literally everything in any and around every given space the list of individual variables is near endless. Copper however is the most reactive of common coinage metals meaning it tones more and faster than other common coinage metals. Common is the operative word here because there are other coinage metals that are even more reactive than copper but they are not common by standard definition, metals like manganese brass, zinc, and aluminum.