If I check the version of my ZenPhoto, it says I have version 1.4.4.3. I did download 1.4.4.5 here and tried the update through FTP and so on as explained here but when doing the setup.php I got all kind of errors which I did not understand at all. I had a backup and placed it back and all works fine again.
I noticed now also there is an check_for_update plugin and I enabled that. But how does it work from there on? The plugin is active but how does it work?

The plugin detects if there is a newer version available and if so shows a notice when you are logged in.

It does not update your installation.

Ah ok! But where is that notice then? I do have a part on the first admin page where it says "News from zenphoto.org" but there it says: "Failed to load Ophalen van de link http://www.zenphoto.org/index.php?rss=news&withimages mislukt."

And okay, then I can only use the Installatron app that my host is offering for application install to keep ZenPhoto up to date.

You have to logout and then login again to see the notice.
It appears just below all the admin tabs.

Nope, can not see it. Don't know what you mean with Admin Tabs though? I log in, I see tabs. The first one contains info on the current version, backup/repair and so on. But nothing that shows there is an update ...

Ah yes, the plugin only checks every 20 days.
So, once a notice is shown it will not show up again until 20 days later.
Maybe you overlooked one.

Anyway, the weird thing is that you cannot update your install manually.
Maybe ask your host what's happening or ask them to make the latest release available via Installatron.