There are 2 ways to edit the site config when you have multiple sites:
1. Switch the site from the top admin bar and select "Edit global site settings" button at the top of the site tree
2. Select Manage Sites from the top admin bar, and click the edit icon for the required site
If you do (2), then although you will be editing the record for the chosen site, any site tenancy on the config form will be based on the currently active site.
So, if the active site is Site A, and you choose to edit Site B from Manage Sites; then, if for instance you have a sitetree picker on the form, it will be populated with data from Site A. The same applies for any other site-tenanted pickers on the admin form.
When editing a site config, the ID of the site being edited should act as the active site for any site-tenanted controls.