If a user override is made by the teacher during a quiz attempt in Moodle (e.g.: 10 minutes extra time for students due to technical problems), it will only take effect when the page is reloaded - either by switching pages or when reloading a page.
As a teacher, I would expect any user override to be immediately displayed to students. Therefore, especially for the essay, a save button would be helpful to trigger a page reload.

Testing instructions:
1) Create a new quiz with a time limit and an automatically submission. Add at least two questions but no page change.

2) Attempt the quiz as a student.

3) As a teacher, perform a user override (10 minutes extra time) for the student while the quiz is in progress.

4) As a student: Don`t reload the page or switch the page –

Result: The test is automatically submitted at the original time and the extra time does not take effect (see screenshots 1 and 2).