In my opinion, public humiliation, which you claim is one objective of exposure is a punishment, or revenge. To say that it is not, is splitting hairs.
In the case of the pain caused by the cheater to his spouse, that is collateral damage. It is an accidental result of the action he has chosen to take. While it is possible that someone might cheat and flaunt it against the spouse, usually they go to some trouble to try to hide the affair.
In the case of public humiliation, that is a deliberate action, intended to cause pain and embarrassment to the other person. It cannot be construed as unintended.
