Some other user described his problem over an email and helped me to reproduce the issue here.
TotalFinder’s Dock icon stops opening new TotalFinder window if you previously had a TotalFinder window with multiple native Finder tabs and closed it. Not sure why is this happening, probably one of Finder’s tabs stays in some weird state and clicking the Dock thinks it is still on-screen so it does not create a new Finder window. Something like this.
Anyways, a workaround is to force-quit Finder.app via CMD+OPT+ESC and launch
/Applications/TotalFinder.app again. To prevent this situation in the future, please makes sure you have unchecked
Finder -> Preferences -> General -> "Open folders in tabs instead of new windows"