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Sorry, here is the screencast - http://screencast.com/t/rmAE3xB0XA
Here is a video showing the problem. 

At the start you can see me moving the mouse around but no icons show up. That is because the window isn't active yet. On the Mac the window doesn't active until you click on it. So you have to click and then move the mouse around before the icons show up.

At around 0:08 you can see me deleting rows, but the trash icon doesn't show up for the next row right away. Instead I have to jiggle the mouse to get it to show.

At around 0:19 I click outside the window so its no longer active. Then you can see me trying to get the action icons to show up. They won't because the window isn't active. So I once again have to click inside the window and then move the mouse around to get them.
I definitely have to wiggle and its a real pain. This is on Chrome on OSX.

Really I would like an option for the icons to just always be visible. Both the delete and the action icons in the corner. Right now I have to active the window and then move my mouse a bit to do anything. Its a real pain.
While this is declined, I think many still agree the scrolling could be better as described in http://tabsoutliner.userecho.com/topic/133351-option-to-turn-off-scrolling-or-just-show-the-whole-tree-when-theres-only-a-few-tabs/
I agree with what Steven said. The problem isn't that it scrolls, its that it always scrolls the tab to the top.  If its the last tab it hides everything else. Instead it should scroll only enough to show it.