The code itself does not appear to have any error. I modified your code a little bit to work with real table/column I have, and it worked for me:

use DBI;
use Data::Dumper;
use strict;
use warnings;

my $dsn = "DBI:mysql:database=test;host=foo";
my $dbh = DBI->connect($dsn, 'root', 'bar', {RaiseError => 1});
my $data = qq(SELECT person FROM or_mod);
my $sth = $dbh->prepare($data);
$sth->execute() or die $dbh->errstr;

my @a;
while(my $ref = $sth->fetchrow_arrayref) {
    push @a, $ref->[0];
}

print Dumper(\@a);
[download]

The loop part actually can be changed to a map:

my @a = map {$_->[0]} @{$sth->fetchall_arrayref};
[download]