I confirmed this by adding an extra scope. That would fix the problem I've observed before.

sub count_up {
{
    .
    .
    .
}
}
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$cnt=0; $progress=0
$cnt=0; $progress=20
$cnt=0; $progress=40
$cnt=0; $progress=60
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Turns out the variable is always different than the one in the previous call to the function. (As it should be since we keep creating external references to it.)

my $r = \$progress;
print("address of \$progress=$r\n");
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$cnt=0; $progress=0
address of $progress=SCALAR(0x19fc970)
$cnt=0; $progress=20
address of $progress=SCALAR(0x19fe710)
$cnt=0; $progress=40
address of $progress=SCALAR(0x1cfdb0c)
$cnt=0; $progress=60
address of $progress=SCALAR(0x1d13fc4)
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That means something is setting the new variable to the value the old one had. It must be configure.

    $pb->configure(
        -from => 0,
        -to   => 20,
        -variable => \$progress,  ## store the reference.
    );
$progress = 0;
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$cnt=0; $progress=0
$cnt=0; $progress=0
$cnt=0; $progress=0
$cnt=0; $progress=0
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I confirmed this by looking at the source. Note $$varref = $oldval;.

sub variable {
    my $c = shift;
    my $oldvarref = $c->{'-variable'};
    my $oldval = $$oldvarref if $oldvarref;
    if(@_) {
    my $varref = shift;
        if ($oldvarref)
         {
      $c->traceVdelete($oldvarref);
         }
    $c->{'-variable'} = $varref;
    $c->traceVariable($varref, 'w', sub { $c->value($_[1]) });
    $$varref = $oldval;
    _layoutRequest($c,2);
    }
    $oldval;
}
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use strict;
use warnings;

use Tk;
use Tk::ProgressBar;

my $mw = MainWindow->new(-title=>"Bug Demo");

my $progress;
my $pb = $mw->ProgressBar(
    -width    => 20,
    -length   => 200,
    -blocks   => 20,
    -from     => 0,
    -to       => 20,
    -variable => \$progress,  ## store the reference.
)->pack();

my $button = $mw->Button(
    -text => 'Press this!',
    -command => \&count_up,
)->pack();

MainLoop;


sub count_up {
    $progress = 0;
    $mw->update;
    for (1..20) {
        select(undef, undef, undef, 0.01);
        $progress++;
        $mw->update;
    }
}
[download]