You can simplify all the dereferencing if you use a while loop with each rather than a for loop. With this method, you cannot sort the keys, but in your case, that is OK.

use strict;
use warnings;
use Test::More tests => 2;

my $month_total    = 0;
my $day_week_total = 0;
my $VAR1 = {
    'Adam' => {
        'days'  => 22,
        'weeks' => 5,
        'total' => 22
    },
    'Keas' => {
        'total'  => 114,
        'test'   => 2,
        'weeks'  => 8,
        'days'   => 107,
        'months' => 5
    },
    'Tim' => {
        'total'  => 4,
        'weeks'  => 5,
        'days'   => 3,
        'months' => 1
    },
    'Sum' => {
        'total'  => 440,
        'days'   => 365,
        'months' => 9
    }
};

while (my ($name, $hash) = each %$VAR1) {
    next if $name eq 'Sum';
    if (exists $hash->{months}) {
        $month_total += $hash->{months};
    }
    if (exists $hash->{days} and exists $hash->{weeks}) {
        $day_week_total += ($hash->{days} + $hash->{weeks});
    }
}

ok($month_total == 6, 'month_total');
ok($day_week_total == 150, 'day_week_total');

OUTPUT:
1..2
ok 1 - month_total
ok 2 - day_week_total
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