That clobbers the parent's $_. Fixed:

sub get_oligo_seqs{
    my ($fh) = shift;
    my @seqs;
    while(my $rec = <$fh>){
        my @fields = split /\t/, $rec;
        my $oligos = $fields[1];
        push(@seqs,($oligos));
    }
    return @seqs;
}
[download]

This seems simpler to me:

sub get_oligo_seqs{
    my ($fh) = shift;
    my @seqs;
    while(my $rec = <$fh>){
        push @seqs, ( split /\t/, $rec )[1];
    }
    return @seqs;
}
[download]

Why stop there?

sub get_oligo_seqs{
    my ($fh) = shift;
    return map { ( split /\t/ )[1] } <$fh>;
}
[download]