No. The IRS goes by physical custody, not legal custody . "Joint custody" is a legal custody term.
There's a chance you ex has been given some bad advice. When physical custody is even (exactly 183 nights each, in a leap year), the rules state that the parent with the higher income has the higher priority on claiming the kids. He may be thinking that "joint custody" gives him the right to claim them, because his income is higher than yours. It doesn't. Your "the children being with me more" trumps his "joint custody" and "makes more than I do".
