teitbite Thank you for your kind and indeed professional answer. That's right, that must be the case for your demo site.
In the meanwhile I found out what the problem is with my own case, I think: it has to do with the "popular tag" module: the point is, tags don't seem to support multilanguage at all. Therefore, tags language need to be set to ALL. Now, the Tagged-Items menu item language also has to be set to ALL.
Otherwise, the tags grouped by the "popular tag" module won't display the items retrieved in the intended menu item, which is, Tagged Item menu item.
I know it hasn't directly to do with the template you provide, but who knows, that may be useful for someone else too, it took me a lot to find out.