when a student uploads a file it triggers an event.
when cron runs it sees that event and if turnitin is enabled for that assignment it will add a record to the plagiarism_turnitin_files table for that file and will submit the file to turnitin.
If you have previously installed another plagiarism plugin like crot/urkund/compilatio/moss that go into the /plagiarism directory but you have deleted the files there may be an event handler in your database that is holding up the event from being handled by Turnitin. The handlers in the table look for the code that created the handler (eg crot/urkund/compilatio) and if it can't find the code it causes that event type to "hang" completely in your database. the fix is either to restore the deleted files in which case it will see that the assignment hasn't been configured to use that plugin and clear or you will need to manually remove the invalid handlers from the handlers table.
The latest turnitin code will show an error on the turnitin settings page if there are any invalid handlers in the db.
IF the students submitted the files before you enabled turnitin inside the assignment - those files will not be sent to Turnitin - only files uploaded after turnitin was enabled in the assignment will be sent.