After I made the phtml template work, I've got now the problem, that changes in the template are not applied.
If I change its content, I see still the content of the old template version.
I see in the database, that there is still the old content in the core_theme_templates table, even if I clear all caches.
So it looks like this update mechanism is kind of broken, at least on development instance.
Again, if I download the plugin, then delete it and upload it again, everything workds and gets updated.
If I change the template file in developer mode, nothing gets updated . . .