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No, there is no automatic notification. If you set the Post Date to the expected Post Date, and stick to that, then students will know (from the Turnitin Assignment's landing page aka Summary) when to check back. Otherwise, tutors can always send a News Forum post saying ‘Your marks are now available to view’.
When I click on the pencil icon to view or grade a submission, I get a notice 'Loading error: This paper is not available. M14: 11'
There is currently a bug which will not allow you to access submissions this way. Please click on the title of the submission in the inbox, this will load the paper correctly.