The due date of the assignment reminds students to complete the assignment in time. When peer reviews are enabled students don't have an indication or reminder to complete the peer reviews before a certain date and time. When a teacher wants to access the given reviews, it would be necessary that the reviews have been added by students before the scheduled date and time.
Add a reviews due box with which a date and time can be entered:
Also have this due date reflected in the To Do Lists and trigger notifications based on the user notification settings.
The guides How do I know if I have a peer review discussion to complete? and How do I know if I have a peer review assignment to complete? currently contain the text: Note: Currently the Due Date in the To Do List does not accurately display the due date for completing your peer review. If details about your peer review are not already included in the details of your assignment, please contact your instructor.
This would removes the confusion about the date in the To Do list and the notes in these guides could then be removed.
Note: please also vote for Respecting sections when automatically assigning peer reviews