When you create a Turnitin Assignment, you have to set three types of dates:
Start Date - the earliest date students can submit. This is when the assignment opens to the students, before this date they can see the assignment but they cannot upload their file(s).
Due Date - the deadline. After this date, the students cannot upload their file(s) anymore. If you have enabled late submissions any late submission will appear in red.
Post Date - the date that marks and feedback are returned to students. Two things to keep in mind about the Post Date: one is that it must be the same as or later than the Due Date and the other is that it can be changed (as long as it hasn't already passed).