I've got no idea what to make of that; if, as it sounds, it's a brand new situation, maybe you ought to "Report a Problem" from CCC's Help menu.
Did CCC insert itself into your FDA pane, or did you select it?
As I said, I haven't got CCC in either FDA or Accessibility, and I clone to both internal and external drives.
Update: I took a look in CCC's documentation (and saw the fish for the first time), and it turns out that it does need full disk access, and a chance look at CCC's menu bar disclosed that my installation has got it, despite the fact that it doesn't appear in my FDA pane. 
