Some people automatically flee from conflict. Perhaps they run away like a frightened child or flounce off with a flourish in a huff, or storm out angrily!
What should you do?
Let them walk away and then arrange another meeting, informing them that it is inappropriate to walk out of a meeting about work; such a meeting is a reasonable management request and walking out before it has concluded could result in disciplinary action. Let them know that disciplinary action is not the intention at this stage as it’s happened once, but warn them that disciplinary action is possible should it happen again. I would follow up this reprimand in writing, making the point that the letter is not part of any formal process. I include this sentence at the end of such an email in case the situation repeats or escalates and your account is challenged at a later date:
“Please let me know by the end of this week if you feel that this is not an accurate record of our meeting.”
You could do the above fully in writing but my preference is face-to-face, if possible, with a written follow-up.
You need to establish that their behaviour is not an acceptable response and that there are consequences. These consequences are not going to be applied this first time, but if it happens again then they know what might follow.
And do speak with your Human Resources/Personnel support before taking actions like this.