I’m not sure if is this that you need, but try to “explode” it…
<?php
// Headlines variable can control admin area
// Does this return the string "2,3,4,5" ???
$headlines = get_option('t_turmanset');
query_posts( array( 'numberposts' => 4, 'post__in' => explode(",", $headlines) ) );
if ( have_posts() ) : while ( have_posts() ) : the_post();
?>