You should not be returning a hashref from your get() method. It completely negates the purpose of using InsideOut objects.

Try this:

package InOutObj;

use strict;
use warnings;
use Scalar::Util qw( refaddr );
{
    my( %upper, %lower );

    sub new {
        return bless \do{ my $dummy }, shift;
    }

    sub getUpper {
        my $self = shift;

        return $upper{ refaddr $self };
    }

    sub getLower {
        my $self = shift;

        return $lower{ refaddr $self };
    }

    sub set {
        my ( $self, $arg ) = @_;

        $upper{ refaddr $self } = uc $arg;
        $lower{ refaddr $self } = lc $arg;
        return;
    }

    sub DESTROY {
        my $self = shift;

        delete $upper{ refaddr $self };
        delete $lower{ refaddr $self };
        return;
    }
}

1;

package main;

use strict;
use warnings;

my $obj = new InOutObj;

$obj->set('i LiKe WiNe');

# User should not be able to make up stuff on their own!
print $obj->getUpper . "\n";
print $obj->getLower . "\n";
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