What is the legal ruling on describing a person as ignorant during a verbal altercation about the prohibition of fortune-telling (reading the cup), and what is the optimal course of action in such situations?

Fortune-telling by reading coffee cups is a form of divination (كهانة) forbidden by Sharia. The caller to Islam (داعية) must be wise in his call, use a good approach, and avoid anger. You should apologize to your aunt and explain that your action was motivated by your concern for her guidance away from the serious matters of divination.