I think your wife was in all likelihood already in at least an EA with this man when she asked you for your separation.
Let me ask you, when she told you "she was going to see others," how did you respond? If you laid down a boundary, because you were still married, then yes, she is considered to be having an affair. If you were OK with it, then I guess you'd be considered to have an "open marriage." Personally, I would never be OK with that.
