When an iOS device is connected via Remote Debugging, your machine will treat it as if it is connected locally via USB.
This allows Safari to see the device as locally connected which is why it then enables you to debug your mobile site.
When debugging mobile sites using Safari on Mac, Safari must be closed before the Remote Debugging session is initiated. Since it is not possible to keep a remote debugging session active when the browser is closed :
1. You should use Chrome to open the device and initiate the Remote Debugging session
2. And only then open Safari - and the developer tools.