Greetings,
from the screenshots you sent, the theme you’re using changes its layout when it’s displayed on mobile devices.
Most likely the theme has two headers/menus, one for mobile and one for desktop. This is a lazy programming technique some developers use, as it’s easy to style these headers/menus. The theme dynamically duplicates the menu (via javascript) for mobile devices. But it’s unable to duplicate the translator (because of its complexity) or by the time it duplicates the header/menu the translator hasn’t been initialized yet.
The easiest “solution” would be to place the translator in an area that’s not duplicated by the theme. The other solution would be to ask your theme developer to have one single header/menu.
I hope you understand that this is an issue created by the theme and not by the translation plugin itself.
Regards