the text in the progress window appears in the middle of the window.

There is no need to create/destroy labels, this is how you should write that

#!/usr/bin/perl --
use strict;
use warnings;

use Tk;
use Tk::Pane;

my $mw = MainWindow->new();
$mw->geometry("100x100");
$mw->Button( -text => "START", -command => \&start_computation )->pack
+;

MainLoop;

sub start_computation {
    my $progress = $mw->Toplevel();
    $progress->geometry("100x100");
    my $pane = $progress->Scrolled(
        'Pane',
        -scrollbars => 'osoe',
        -background => 'red',
      )->pack(
        -fill   => 'both',
        -expand => 'yes',
      );
    my $text = "Computation started...\n";
    my $label = $pane->Label(
        -textvariable => \$text,
    )->pack(
        -side => 'right',
    );

# doing several computation steps
    for my $step ( 1 .. 10 ) {
        sleep(1);
        $text .= "Step $step finished.\n";
        $pane->update;
    }

    $text .= "\nComputation finished.\n";
    $pane->update;
    $pane->Button( -text => "QUIT", -command => sub { exit; } )->pack(
        -anchor => 'nw',
    );
    return;
} ## end sub start_computation
[download]

It doesn't fix the centering/layout issue, maybe this tutorial can help