Automatically change input source
Here's what I'm experiencing on El Capitán...

The key here is "document's input source" so when switching from Skype to Safari, if no document (web page in this case) has focus the input source will not change. If you then select, for example, a field on a page, the input source should change to whatever the last input source was when you were last in that document. So one application program can have multiple documents each with its own input source and the OS won't switch input sources until a specific document within the app has been selected.

If you open a new safari window or tab, the currently active input source will be used for that new "document."