Move out notice

[Li Kia]

I have a question about a move out notice. My tenant wrote me an email on 5/12/24 saying they were moving out but move out date could be 6/8-6/12, they would let me know soon. On 5/17/24 they said their move out date is 6/12. They are on month to month with 30 days notice. They paid last month rent. They moved out 6/13/24.  I refunded them the remaining rent for 6/18-6/30. However they said it should be 6/14-6/30. Which one is correct? I thought the move out date starts when they told me the exact move out date. Am I wrong ?  They texted and called multi times daily asking for more money.