Actually, it appears to be the other way around. And here's an even simpler way (no need to split):

#!/usr/bin/perl

use strict;
use warnings;

my @filenames = qw/Reg Irreg/;
my %ofh =
    map { open( my $fh, ">", $_.'ularOlios.txt' ) or die $!; $_ => $fh
+ }
        @filenames;

while (<DATA>) {
    my $o = ( /^\w+-/ ) ? $ofh{Irreg} : $ofh{Reg};
    print $o $_;
}
close $_ for ( values %ofh );

__DATA__
10002TU    AGACATTACCTGTGAGACACCTTTC GCCTCCACCTCAGAGTCAG      TCCATGGG
+AAGGATCTCCGTGAAATCA
10002TU-2  GCTCCAGCTAGAAGAGAATCC     CCCACCAGGGCTGTGTAAG      CCTGTGAG
+ATAGTACAGCTGAAGAGTTGGC
10002TD    TGTGTTGATTCTCAGCCTCTTG    GACGGAGCACATAGGCAAAG     TCTGTTCT
+TCTCAGCTGTCTTTGTTGCTGC
10003TU    CAGCAAGCCCTGAGGTGTG       CAGTGAACTGAGAAAGACGAGAGG TGCAAGTC
+CAGATGGAGGCCACC
10174TU-2  ACCTGAACAGCCTGACATGAAC    TGGGATGGAGGGCAAAGTC      CCACCTAG
+TATGACCCAGCACACCTCC
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