I don't use the getmail plugin so I can't really comment on the setup but maybe I can give you some hints as to whats wrong.
In fact, nothing happens. I do not know PHP language but I added :
echo $rcmail;
just after the line
$rcmail = rcmail::get_instance($GLOBALS['env']);
in the file cron.php, and I executed it manually.
$rcmail is empty. I do not know what rcmail::get_instance() is doing but I see this statement in the Plugins Resources page in your website.
I suspect the getmail plugin cannot work with $rcmail empty ...
The get_instance function is being used to start Roundcube, the reason why it seems empty when you echo it is because it returns an object not a string. If you wanted to see the contents you would need to do the following:
echo print_r($rcmail, true);
I also tried to debug this...
the error is in rcmail::get_instance($GLOBALS['env']);
somewhere in this a die() without message is thrown.
Also added
error_reporting(E_ALL);
ini_set('error_log', '/var/log/php-error-shell.log');
error_log('hello');
but only log is
[17-Dec-2015 15:11:44 Europe/Berlin] hello
Most likely there isn't any fail errors being thrown and thats why changing the error reporting doesn't show anything more.
did in one of the last versions
rcmail::get_instance
change?
If your using the GIT version of Roundcube then yes the function has changed, if your using Roundcube 1.1.x then the function hasn't changed.
My gut feel is that the problem is something deeper in the plugin then the initialization.