You had all the pieces, just need to alter them slightly:

use warnings;
use strict;

my @files = qw(
    aaa_bbb_10.ddd.eee
    aaa_bbb_11.ddd.eee
    aaa_bbb_12.ddd.eee
    aaa_bbb_13.ddd.eee
    aaa_bbb_14.ddd.eee
    aaa_bbb_15.ddd.eee
    );
my $min = 12;
my $max = 14;

my @filtered = map {$_->[0]}
    grep {$_->[1] >= $min && $_->[1] <= $max}
    map  {my ($time) = /(?:[^_]*_){2}(\d+)/; [$_, $time]}
    @files;

print "@filtered";
[download]

Prints:

aaa_bbb_12.ddd.eee aaa_bbb_13.ddd.eee aaa_bbb_14.ddd.eee
[download]