If you are using the TurnItIn direct plugin I dont think you will get it to work as, although it looks like you are submitting in Moodle you are actually connecting directly to TII and Moodle does not have visibility of those actions.
An alternative approach would be to use the core Moodle assignment type with the TII plagiarism plugin:
https://moodle.org/plugins/plagiarism_turnitin
That will integrate TII into the core assignment type, allow staff to use TII grademark / feedback studio and fetch back the grades.
It will also allow you to use completion tracking properly.
