If your stbx can show that this person alienated your affections from him, that you had a viable marriage (meaning without this persons interference you would still be “happily” married)he can file suit against him for alienation of affection. It is expensive to sue for this and time consuming, aggrivating. From what I’ve read on these forums, an attorney will write a letter “threatening” a lawsuit unless a settlement is reached and if the person in question is guilty, they usually pay a settlement to keep it from court. If there is nothing to prove, then it can go to court and be decided if this person had anything to do with the demise of your marriage.
Criminal conversation or adultery is a misdemeanor and is the actual act of sex with someone other than your spouse. There is a 3 year statute of limitations after knowledge of the act. Though it is rarely prosecuted, it is illegal and it can have an affect on alimony.
On a side note, it sounds to me as though your stbx is probably blowing smoke to “scare” you into signing an agreement or getting you to give in on something that he wants…don’t respond. Don’t get worked up unless you see an official court document…and if there is nothing to the accusation, then don’t let it worry you any more.