D'oh! Late waking up this morning. That's because hashes can only have unique keys... you can create a hash of arrays to fix this issue:

#!/usr/bin/perl
use warnings;
use strict;

use Data::Dumper;

my %h;
my @a;

while (<DATA>){
    chomp;
    my @a = split /@@@/;
    push @{ $h{$a[0]} }, $a[1];
} 
print Dumper \%h

__DATA__
CustomerA@@@DomainA
CustomerA@@@DomainB
CustomerA@@@DomainC
CustomerA@@@DomainD
CustomerA@@@DomainE
CustomerB@@@DomainA
CustomerB@@@DomainB
CustomerB@@@DomainC
CustomerB@@@DomainD
CustomerB@@@DomainE

__END__
$VAR1 = {
          'CustomerB' => [
                           'DomainA',
                           'DomainB',
                           'DomainC',
                           'DomainD',
                           'DomainE'
                         ],
          'CustomerA' => [
                           'DomainA',
                           'DomainB',
                           'DomainC',
                           'DomainD',
                           'DomainE'
                         ]
        };
[download]

Then access everything like this:

for my $key (keys %h){
    for my $elem (@{ %h{$key} }){
        print "$key: $elem\n";
    }
}
[download]