On the Summary screen (the first of 4 tabs the tutor sees when they click the link to the assignment) there is a pencil icon. Clicking this allows editing of the dates and times. You then need to click the tick icon (which replaces the pencil) to confirm the changes.
The graphic above shows the screen (click the image to show it full size), which I notice has lost its labels:
The leftmost entry (11:49) is the start time and date. No submissions may be made before this.
The middle entry (12:00) is the due date or deadline. No submissions will be allowed after this.
The rightmost entry (09:05) is the marks posting date, after which marks will be made available to the students.
The text field containing “Part 1” is used to distinguish between seperate submissions if the assignment requires more than one file to be submitted. You can normally safely ignore this.