NotesTools uses the tsutil.nsf database to work out which database you're in. Without this tsutil.nsf database you would be prompted with the "which database" dialog box.
tsutil.nsf appears to be empty but it contains just one agent and nothing else.
When you're in your Notes workspace and click on one of the tool icons, you'll notice that it switches to the tsutil.nsf database. The NotesTool icon has just called the agent in tsutil.nsf to see if it can tell which database you're in and pre-populate the NotesTool dialog with the database server and file name.
If you're already in a database then you don’t see this behavior
In NotesTools Edition 32 (build 4977), the installer puts tsutil.nsf in the root of the <NotesData> directory. Unfortunately the code was still looking for tsutil.nsf in the <NotesData>\TeamstudioDocs directory.
This has been addressed in Edition 32 (build 4978). This edition fixed this issue. It now looks for it in the root data directory where the installer puts it.