Automatic forwarding is something that should be done by your mail server, not by a client like Roundcube. If the forwarding is done client side then it only works when the client is open.
In the screenshot you saw may be the managesieve plugin (shipped with Roundcube) was active. This plugin provides a management interface for sieve filtering on the server - so if its right for you depends on if your server supports sieve and the managesieve protocol.
