G'day saw55,

Welcome to the Monastery.

I see the reason for your problem has been explained by ++jcb.

Instead of calling exit(0) as you currently do, consider passing a flag that instructs &timedDialog to either destroy the dialogue or exit the application.

Here's a fully functional, albeit extremely barebones, example of what I mean.

#!/usr/bin/env perl

use strict;
use warnings;

use Tk;

{
    my $mw = MainWindow::->new();

    $mw->Button(
        -text => 'Transient message',
        -command => sub { out_msg(\$mw, 'Message ...', 2_000) },
    )->pack();

    $mw->Button(
        -text => 'No backup',
        -command => sub { out_msg(\$mw, 'Exiting ...', 2_000, 1) },
    )->pack();
}

sub out_msg {
    my ($mw_ref, $msg, $delay, $exit) = @_;

    my $tl = $$mw_ref->Toplevel();
    $tl->Label(-textvariable => \$msg)->pack();
    my $handle_msg = $exit
                   ? sub { exit }
                   : sub { $tl->destroy };
    $tl->after($delay, $handle_msg);
}

MainLoop;
[download]

Note that the flag is only needed for those callbacks where you want to exit: you may only need to make minimal changes if you adopt this technique.