Stevie claims she was the one who broke up with Joe, but it was indeed during that time period. Here's her story (C&Ped from the Stevie and Joe thread):
"What happened at the end was I was getting ready to cut two songs with Waddy Wachtel producing and we only had two nights to rehearse and Joe had been off in New Zealand or something and he came down about one or two in the morning or something and he was real good friends with everyone in my band. That would have been fine any other night but I was really angry with what Joe had done because he completely screwed up that session. He just had everyone dying laughing because he just tells a hundred jokes and everyone was just rolling in the floor laughing and I was going “this is not fair” because he is not being sensitive at all to this whole situation and “you know I would give up anything for you, even my dammed career for you if he was serious enough."
I had a limousine and I asked Joe if he wanted to take me home or me to come home with him and he said, “Well, I didn’t tell you this but I’m leaving for Australia like tonight and I have to pack, so I’m just going to get a ride home with Waddy.”
And I said “Ok” and started walking towards the door, and I turned around and said, “Joe I don’t like where this relationship is going 'cause it’s not going anywhere and I don’t want to do it anymore.” And I started walking towards the door and he said, “Well, you know, if you walk out the door, you basically cease to exist.” And I just didn't stop walking."
BBC Interview with Nicky Horne ~ August 27, 1991