Here is a complete runnable example, that demonstrates the problem:

use strict;
use warnings;
use Tk;

my $mw = tkinit;
my $frm1 = $mw -> Frame(-bg=>'LightSkyBlue1') -> pack(-fill => 'x');
my $frm11 = $frm1 -> Frame(-bg=>'LightSkyBlue1') -> pack(-fill => 'x')
+;

my $lst = $frm11 -> Scrolled('Listbox',
                              -width => 50,
                              -height => 5,
                              -scrollbars => 'oe',
                              -selectmode => 'single') -> pack();
$mw->update;
$lst -> delete ('0.0', 'end');
$lst -> insert('end',(0..10));
$mw->update;
# force scrollbar refresh:
#  my $sb = $lst->Subwidget('yscrollbar');
#  $sb->set( $sb->get );

MainLoop;
[download]

That works! Thank you!