Here's an example of Tk::IO

You'll have to write a separate perl program to fetch URLs. In this example I faked that part with a simple shell script just as a proof of concept.

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1227829

use strict;
use warnings;
use Tk;
use Tk::IO;
use Tk::ROText;

my (@data1, @data2, @data3, @data4);
my $complete1 = my $complete2 = my $complete3 = my $complete4 = 0;
my $status = 'Ready to Start';

my $mw = MainWindow->new;
$mw->Button(-text => 'Load', -command => \&startload,
  )->pack;
$mw->Label(-textvariable => \$status,
  )->pack;
$mw->Button(-text => 'Exit', -command => sub{$mw->destroy},
  )->pack(-side => 'bottom');
$_ = $mw->ROText( -width => 40,
  )->pack(-side => 'left') for my ($t1, $t2, $t3, $t4);

MainLoop;

sub startload
  {
  $status = 'Started';
  child( \@data1, \$complete1, 'one', 'sleep 1; echo data one', $t1 );
  child( \@data2, \$complete2, 'two', 'sleep 3; echo data two', $t2 );
  child( \@data3, \$complete3, 'three', 'sleep 4; echo data three', $t
+3 );
  child( \@data4, \$complete4, 'four', 'sleep 2; echo data four', $t4 
+);
  }

sub common
  {
  $complete1 && $complete2 && $complete3 && $complete4 or return;
  $status = 'All Completed';
  # do final processing here #####################
  }

sub child
  {
  my ($refdata, $refcomplete, $message, $command, $rotext) = @_;
  @$refdata = ();
  $$refcomplete = 0;
  $rotext->delete('1.0' => 'end');
  Tk::IO->new(
    -linecommand => sub {push @$refdata, shift},
    -childcommand => sub {
      $$refcomplete = 1;
      $status = "$message completed";
      $rotext->insert(end => join '', @$refdata);
      common();
      },
    )->exec($command);
  }
[download]

There are a couple other examples of Tk::IO on this site, you can search for them if you want.