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.