Assignments are not created on Turnitin.com if there is no "Available from" and "Due Date" selected in the assignment creation.

Re-creation:
Create new course.
Add an Assignment. Advanced Uploading of files.
Disable "Available from" and "Due Date".
Select Use Turnitin submission.
Save

Assignment not created in Turnitin.

Cron error message:
Error occured in Turnitin System:Class does not exist in Turnitin database for account.
Please contact your instructor for further details. tiicode:204

With enabled "Available from" and "Due Date" course is created and assignment can be submitted.