It's the first time I see this behaviour, I see it's working with Safari and Chrome but not with Firefox.
I've noticed that Firefox didn't correctly save the session cookie, that's why it doesn't work. I am pretty sure it's a Firefox bug, it gets confused because in your config.php you named the session "dadabik", which is also the name of another cookie DaDaBIK sets. If you change it to something different than "dadabik" I am sure it will work.