It seems that output order is not necessary for the use-case. The issue mentioned may be coming from say $output (not appending \n to the file for me, instead getting a GLOB message to STDOUT).

Btw, I ran your code and it ran fine. I only changed say $output to print $output "\n"; All files had 10 results -- all identical -- all same size.

Back to MCE, the following processes @input_data in parallel. Am using the MCE::Loop Model versus using the Core API.

use MCE::Loop chunk_size => 1;

my @input_data  = (0 .. 100 - 1);

mce_loop {
    my ($mce, $chunk_ref, $chunk_id) = @_;

    open my $output, '>', "/path/to/my/files/$chunk_id.txt";
    foreach (1..10) { print $output "\t",fibonacci($_)};
    print $output "\n";
    close $output;

} @input_data;

sub fibonacci {
    my $n = shift;
    return undef if $n < 0;
    my $f;
    if ($n == 0) {
        $f = 0;
    } elsif ($n == 1) {
        $f = 1;
    } else {
        $f = fibonacci($n-1) + fibonacci($n-2);
    }
    return $f;
}
[download]

Notice how mce_loop wraps around the serial code to enable parallelism.

Also see https://metacpan.org/pod/MCE::Loop#GATHERING-DATA if wanting to gather data back to the Manager process.