List of values in the "Product" field

Firt, one point that may be confusing is that PRoject in not really directly linked to project.
The relation always comes through project version : you sould link project to product version.
Adding product to project is an accelerator that will automatically link every version of product to the project. But at least one version must exist...

Then, when you know that, you can see that after saving the requirement, product list is empty : this is expected behavior.
Moreover, if you do not select project in project selector, when you create a riquirement and "change" the project, the product list is correct.

What is missing, is that when you select a project in the project selector (and so don't have to change project when creating the requirement), the project list is not correct.
This is an issue recorded as Ticket #2517.