I think I managed to bypass it. I got lucky and went outside for a walk and the weather turned cold, just like when she's about to enter the house, so she probably came and left while I was on that walk.
EDIT: After more testing it seems I can avoid the event by staying outside between 6pm and 12am. Then I spent a few days boosting Jun's sympathy since she had just activated advanced ai until it was enough to take care of the girl.