It's in the same place in that it's on the right edge of the Touch Bar. But when you switch applications, the buttons lengthen and shorten based on the context. Burn in occurs when each pixel is constantly displaying the same thing. In this case, even though the panel as a whole is displaying the same buttons, the pixels themselves are not displaying the same thing.
No, if you set it up to have App Controls with Control Strip, the shortened Control Strip part to the right never moves and stays exactly in the same place unless you switch to the Fn keys, extended Control Strip or the TB turns off.
Still, I don't think it's a problem.