You're not a long way away from what you need to do. twig_roots supplies a reference to a sub to handle matching elements. Consider:

use warnings;
use strict;
use XML::Twig;

my $xmlStr = <<XML;
<config>
 <one id="msn" type="shopping">
   <traffic>
       <daily value="on" />
       <weekly value="off" />
       <monthly value="off" />
   </traffic>
  </one>

 <one id="movies" type="entertainment">
   <traffic>
       <daily value="on" />
       <weekly value="off" />
       <monthly value="on" />
   </traffic>
 </one>

 <one id="espn" type="sports">
  <traffic>
      <daily value="on" />
      <weekly value="on" />
      <monthly value="on" />
      <hyper value="true" />
  </traffic>
 </one>
</config>
XML

my $result = '';
my $twig = XML::Twig->new (twig_roots => {one => sub {oneHandler (\$re
+sult, @_);}});

$twig->parse ($xmlStr);
print $result;


sub oneHandler {
    my ($resRef, $twig, $elt) = @_;

    $$resRef = join ' ', $$resRef, $elt->att ('id');
    return;
}
[download]

Prints:

 msn movies espn
[download]

Note that there were a few missing close " in your sample XML that I've fixed.

Also notice that I created an anonymous sub so I could pass extra parameters into the handler thus avoiding the need for global variables.