I've played with Tree Style Tabs, but it seems like there's some configuration required for the optimal result. So I ask: have you done any configuration changes to it?
I also shrink it down when the mouse isn't over it. See the screenshots for mouse out and mouse over look.
Mouse not over tree tabs: https://i.imgur.com/ikQhxTM.png Mouse over tree tabs: https://i.imgur.com/TyRds6V.png
Works well for me.
This is what I'm using right now - https://pastebin.com/bKHM8hp9