The one-touch resolution calculation counts any solved or closed tickets with less than two agent replies.
In Explore, the metric you should use to make this calculation is One-touch Tickets. For more information, see the article: Metrics and attributes for Zendesk Support.
If a customer re-opens the ticket with an additional question and the agent responds and solves the ticket again, it will no longer count as a one-touch resolution.
However, if the customer reaches back saying 'thank you' for example, and the agent solves the ticket without making another reply, the ticket will still count as a one-touch resolution.