Thank you for posting!
In short, the behavior you describe is expected and can affect anyone disconnecting and reconnecting an external display from a Windows 10 system (even when Plugable products are not in use). We are not aware of a workaround for this behavior when using Windows 10, however the next version of Windows (Windows 11) appears to have a solution.
To expand further, when you disconnect an external display from a Windows 10 host PC (as you are in effect doing when pressing the button on your USB Sharing Switch) Windows will ‘move’ all of the open application windows that were located within the external display to a display which is currently connected and active.
Unfortunately, when you ‘reconnect’ the external displays (such as when you use the USB switch again) Windows will not ‘move’ the application windows back to their previous location on the external displays.
This is a known limitation of Windows 10 which Microsoft is addressing in the next version of Windows, Windows 11. Microsoft speaks to this feature in this blog post on Windows 11 under the section entitled, ‘Docking’ → https://blogs.windows.com/windows-insider/2021/06/28/announcing-the-first-insider-preview-for-windows-11/
The feature being introduced is within the Display Settings application, and is called, ‘Remember windows locations based on monitor connection’. There is short guide to enabling this feature within Windows 11 here → https://www.elevenforum.com/t/enable-or-disable-remember-window-locations-on-multiple-displays-in-windows-11.47/
When this feature is enabled, application windows will behave in much more helpful and logical manner (as compared to Windows 10) in that applications will return to their original positions on external displays when those displays are reconnected.
In summation, while we unfortunately are not aware of a workaround to the behavior you describe while using Windows 10, the next version of Windows (Windows 11) has a new feature that can help.