I think you may have some confusion about what "current" tiddler the <<currentTiddler>> variable refers to.
It is not about which tiddler is "currently viewed by the user"... rather, the "current" tiddler is the context in which the macro is being processed and rendered by the TWCore. Thus, if I put <<currentTiddler>> into a tiddler named "Foo", and then view that tiddler, the value of <<currentTiddler>> if "Foo", regardless of which other tiddlers are being displayed in the story. Tagging that tiddler with $:/tags/TopLeftBar automatically transcludes it into the $:/core/ui/PageTemplate/topleftbar, which makes that tiddler the "currentTiddler" in the *rendering* process. In your example (putting <<currentTiddler>> into a tiddler tagged with $:/tags/TopLeftBar), it *should* have displayed "$:/core/ui/PageTemplate/topleftbar" in the top left of your document. However, you report that "nothing" appears there, which is not the results I would expect.
In any case, using <<currentTiddler>> won't get you what you want, i.e. the name of the tiddler currently being displayed in the StoryRiver. For that, try using {{$:/HistoryList!!current-tiddler}}, which is automatically updated whenever you open/view a tiddler (i.e., by clicking a tiddler link).
However, there is one relatively small issue with HistoryList!!current-tiddler... it is not updated when you close a tiddler (because it's *only* closing the tiddler, and no navigation to another tiddler occurs at that time). One way to avoid this is to hide the 'close tiddler' in the ViewToolbar control panel settings, so that the user can't actually close open tiddlers. Since you are using zoom-in mode to display tiddlers one-at-a-time, the user can simply navigate to another tiddler, with the *appearance* that the first tiddler is "closed" (even though it's really still in the StoryRiver... just hidden at the moment).
hope this helps,
enjoy,
-e