It was introduced by third-party applications which give multiple people access to a single (or more than one) Twitter account(s). I'm not sure if it was the first to do it, but CoTweet was the earliest that I recall, it would tag tweets with ^CC (initials) based on which CoTweet user account was replying.

Since then it's become fairly standard in customer support, presumably still largely through these third-party apps, but potentially typed manually by some companies as well.