Okay, so here is my taskbar...organized the way I want.
You will notice the mouse pointing to the purple taskbar item, which is a "Groupy" window containing multiple tabs within it.
Also notice that it is in the third position on my taskbar...

Now I will go inside the "Groupy" window, and click on any of the tabs...

By clicking on any of those tabs, my "Groupy" window has suddenly moved to the last position in the taskbar...

This behavior occurs with any Groupy window.
Essentially, switching between Groupy tabs makes the taskbar item behave as if a new window has opened. That is why the Groupy window always moves to the last taskbar position whenever the Groupy tab gets switched.