Result nothing visible happens; that means that the release of a click on the tab-title in 9 didn't make the content-area of the tab in focus; so, the behavior after 6 is not the same behavior like after 9; but there is something that happens even if it is not visible:
Correct. Its subtle but its normal GTK behaviour.
If the tab is not displayed, clicking on the tab switches the tab contents, so the content widget is displayed and selected and so up and down arrow moves the selection _in_ the content.
But if the tab is already displayed then clicking it will _select the tab title_ not the tab content. This may be visible depending on your desktop theme, mine shows a fine dotted line around the tab title. So the first down arrow moves the selection _to_ the content widget, but if you don't notice the selection it will appear that nothing happened. Now the content widget is selected a second and subsequent arrow will move the selection _in_ the content widget.
It is probably easier to see with symbols, when the symbols tab is first made the current tab the filter entry at the top will be selected and have a flashing cursor in it. Press up arrow and the tab title gets the selection and filter entry will lose selection and the cursor, press down arrow and selection comes back to the filter entry.