You are not using true multidimensional hashes. Perl doesn't have true multidimensional hashes. However, it offers two ways to emulate multidimensional structures.
One way is to use references; this is the way you're currently doing it. A reference is like a link or a pointer. When you copy the outer structure, you're just copying a collection of links to the inner structures. The new copy is still pointing at the same inner structures, so altering the inner structures will affect both outer structures.
Perl does offer another mechanism for emulating multi-dimensional hashes. It is barely documented (mentioned in perlvar) and rarely used, but actually works quite well in some situations.
use strict;
use warnings;
use Data::Dumper;
local $; = '#';
my %hash1;
$hash1{'Hello', 'World'} = 1;
$hash1{'Hello', 'Pluto'} = 2;
$hash1{'Goodbye', 'World'} = 3;
$hash1{'Goodbye', 'Pluto'} = 4;
my %hash2 = %hash1; # copy
$hash2{'Goodbye', 'Pluto'}++; # alter hash 2
print "$hash2{'Goodbye', 'Pluto'}\n"; # show that it is altered
print "$hash1{'Goodbye', 'Pluto'}\n"; # hash1 remains unaltered
# Let's see what's going on here...
print Dumper(\%hash1, \%hash2);
perl -E'sub Monkey::do{say$_,for@_,do{($monkey=[caller(0)]->[3])=~s{::}{ }and$monkey}}"Monkey say"->Monkey::do'