The tag has no scrolling feature, please prevent from set the fixed height for the tagbox component. If you really want, please try this code:
$('#tb').tagbox();
var span = $('#tb').next();
span.css('overflow','auto').bind('scroll',function(e){
span.find('.textbox-addon').css('top',0);
var height = $(this)[0].scrollHeight;
height -= span.height();
var top = Math.min($(this).scrollTop(),height);
span.find('.textbox-addon').css('top',top)
})