When creating a new alter, changing the Site ID has no impact on the list of possible alert conditions such as Goals and Custom Reports. The available conditions are set to the site ID in the address bar and are not impacted by the drop down 'Website' menu.
For example, if the site ID in the address bar was set to "1" prior to clicking "Create new alert", only the Goals associated with site ID 1 will be available as alter conditions, regardless of the website selected in the report settings...

