Pantheon Site to Local Environment
Clone the code
Import database
Configure your settings.php file
Get public files; copy them to sites/default/files
Compile CSS and JavaScript in the theme, if it is required
Clear the cache  


Those step should works.

If Backup and Migrate module installed in Pantheon.io
you can get the database and public files from https://pantheon.io/admin/config/system/backup_migrate.