Using the Standalone toolbar has an issue with the select able background of the items, following this article didn\'t work also:
http://blog.mohitkanwal.com/blog/20
This was done using android 5.1 genymotion emulator
I didn't figure out your problem, but I just tried to create a toolbar the same as yours, but with removing some style that I don't have
here is my style
My Toolbar layout
My Menu
The activity code
Toolbar toolbar = (Toolbar) findViewById(R.id.toolbar);
toolbar.inflateMenu(R.menu.menu_home);
Screenshot of the result

Edit
after downloading the sample you provided in the question, the problem has nothing to do with standalone toolbar or actionbar (both have the same problem) when using AppBarLayout, the problem seems that the Ripple effect will be drawn on AppBarLayout instead of the View of the selected menu item, I'll record a video explaining it.
the video: AppBarLayout with Toolbar Video
I'll try to find a solution for this.