Ok, I have a (temporary) solution now. The problem is not mpdf which would use <path to mpdf>/tmp as default directory. osTickets sets an own tmp when instancing the mpdf using sys_get_temp_dir() which is not writeable in my environment. I changed class.pdf.php to use an own tmpdir and created this folder with chmod 777. Now everything works as expected. Unfortunately I don't know a ways to do this without modification.
class Ticket2PDF extends mPDFWithLocalImages
{
var $includenotes = false;
var $includeevents = false;
var $pageOffset = 0;
var $ticket = null;
function __construct($ticket, $psize='Letter', $notes=false, $events=false) {
global $thisstaff;
$this->ticket = $ticket;
$this->includenotes = $notes;
$this->includeevents = $events;
//parent::__construct(['mode' => 'utf-8', 'format' => $psize, 'tempDir'=>sys_get_temp_dir()]);
parent::__construct(['mode' => 'utf-8', 'format' => $psize, 'tempDir'=>'/www/htdocs/xxx/osticket/tmp/']);
$this->_print();
}