Why DOESN'T this Star UML Sequence Diagram have the activation "rectangle" in the Control object? Am I doing something wrong? Should I set something in Star UML?
How can I add the activation "rectangle" in the Control object?
The simple answer is: because that's how the designers of Star UML designed it to be.
In Star UML if nothing initiates (triggers) the Execution Occurrence (that's the formal name of that rectangle) then... there is no Execution Occurrence. If you want to have it, you need to trigger it somehow (e.g. by self-referencing Initiation message).
I didn't find any option to change that behaviour. I haven't been using the Star UML for quite some time but since the free version has been abandoned earlier than I've started using it, I believe nothing has changed since.
If you're using the newer, proprietary version, you can send a request to the dev team of Star UML to add it as a functionality.