You need the yview method, but that fails if there is nothing to be scrolled (if everything already fits), so you need some protection:

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 ();
    my $sp = $progress->Scrolled ("Pane", Name => "Progress",
        -width  => 200,
        -height => 100,

        -scrollbars => "ose",
        )->pack (-anchor => "nw", -fill => "both", -expand => 1);
    my $text = "Computation started...\n";
    my $label = $sp->Label (-text => $text)->pack ();

    # doing several computation steps
    foreach my $step (1 .. 10) {
        sleep (1);
        $text .= "Step $step finished.\n";
        $label->configure (-text => $text);
        my @pos = $sp->yview;
        $pos[1] < 1 and $sp->yview (moveto => 1.);
        $sp->update;
        }

    $text .= "\nComputation finished.\n";
    $label->configure (-text => $text);
    $sp->yview (moveto => 1);
    $sp->update;

    $sp->Button (-text => "QUIT", -command => sub { exit; })->pack;
    } # start_computation
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