I think you need to tie every sub-hash as well, like this:

#!perl

use strict;
use warnings;

use Tie::IxHash;

my $HoHoH = {};
tie %$HoHoH, 'Tie::IxHash';
tie %{$HoHoH->{'alice'}}, 'Tie::IxHash';
tie %{$HoHoH->{'john'}},  'Tie::IxHash';
tie %{$HoHoH->{'andy'}},  'Tie::IxHash';

$HoHoH->{"alice"}{"aaaa"}{"time"} = "20:00:00";
$HoHoH->{"john"}{"ccc"}{"time"}   = "21:00:00";
$HoHoH->{"alice"}{"www"}{"time"}  = "22:00:00";
$HoHoH->{"alice"}{"xxx"}{"time"}  = "22:00:00";
$HoHoH->{"john"}{"aaa"}{"time"}   = "23:00:00";
$HoHoH->{"andy"}{"xxx"}{"time"}   = "24:00:00";
$HoHoH->{"alice"}{"bbb"}{"time"}  = "25:00:00";
$HoHoH->{"andy"}{"yyy"}{"time"}   = "26:00:00";

foreach my $user (sort keys %$HoHoH) {
  printf "%s\n", $user;
  for my $text (keys %{$HoHoH->{$user}}) {
    printf "%s%-5.5s", ' ' x 3, $text;
    for my $time (keys %{$HoHoH->{$user}->{$text}}) {
      printf "%s%s = %s\n", ' ' x 6, $time, $HoHoH->{$user}->{$text}->
+{$time};
    }
  }
  print "\n";
}
[download]

At least it works (for me ;-).
Hope this helped.
CombatSquirrel.

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Entropy is the tendency of everything going to hell.