My husband's affair was carried out at church. At the time he was not living with us due to work, and attending a church by himself in the town he lived.
The OW was his friend's wife, and the pastor's daughter. He had never been attracted to her, or gotten any strange vibes from her. Not until one day when he was in the church kitchen, and she came in and broke down crying, and said she was a "terrible wife." He was taken aback, but had sympathy for her.
They had no contact for a few days, until they met again at a Bible study held at night. After the Bible study they spoke outside, alone, about her marital problems and he confided his problems (of which I was not aware, since he was a poor communicator....except when it came to talking with OW evidently.)
She phoned him later that night, to "give him advice about his marital problems," and then they spoke for 4 hours. By the end of that conversation my husband was hooked on her and within 2 weeks they were committed to leaving their spouses and being together!
She divorced her husband and went on to have more boyfriends, while my husband recommitted to me and we have struggled in our marriage since then.
Your need to make it perfectly clear to your wife that she had better not ever speak with that man, or any other man before or after that Bible study, or you will reconsider whether you want to remain married to her based on her loyalty to your marriage.