Derived from this forum post that solved the problem for me.
Sometimes (most of the time) the limited configuration for TwonkyVision that the MiniNAS config pages gives you isn’t enough. Trying to go to http://yournas:9000 results in the red error page. Apparently LaCie thinks they know better than their users.
To enable TwonkyVision config, upload this signed patch file (mirrored here, in case the original source goes away) in the Configuration page of the MiniNAS config, as an update.
Tested with 220.127.116.11 of the MiniNAS firmware.