To use automatic password fill feature when connecting to ssh host from SSH Config Editor, you need to install a Connector app or use SSH Config Editor Pro version.
Currently SSH Connector supports only Terminal and iTerm2 applications, if you need any other give us feedback.
The apps on the Mac App Store must be sandboxed, it means they can't communicate with other apps or runs scripts so there is no way to implement features like open terminal, run ssh command and fill password in App Store version of SSH Config Editor. We have introduced an optional helper application which makes this features work.
SSH Connector installs itself to ~/Library/Application Support/SSH Connector directory and runs in the background.
Following lines is little bit technical ;)