Ok, I have been screwing with this for hours over several weeks. I give up. It does nto work in the sandbox nor in my lab even when I grant the user permissions to create, view own, edit own, etc. It always saves as the admin creating the record.

Thanks anyways for looking into it.

Do not give up, it is working.

Do not assign any user to any item because it is automatic. This is the wizard !
First to test it, remove the Created By combo from the form.

Then you need to change the virtual user (of the sandbox) BEFORE to create a new item.
Or in your joomla : Log-in with another user. You will see that it works.
It is working for everybody but you.

If it is still not working, please send me your downloaded component through mail (support AT... j-cook DOOT pro)

We will close this ticket today, once your problem fixed.
Cook could also have an issue here, but it is strange on a so simple new project as you describe.