use JSON::XS 'encode_json', 'decode_json';

$pm->run_on_finish(sub {
      my ($pid, $exit_code, $filename) = @_;
      print "** $ident was just written";
      open my $fh, '<', $filename or die "Couldn't read child results from '$filename': $!";
      binmode $fh;
      local $/;
      my $results = <$fh>;
      # Convert results back to the data structure:
      $results = json_decode( $results );

      # now, merge those results with the other results you already have
});

...

for my $task (@tasks) {
    my $filename = "some filename based on $task";
    $pm->start( $filename ) and next;
    ... do the work
    open my $fh, '>', $filename
        or die "Couldn't write output file '$filename': $!";
    binmode $fh;
    print $fh json_encode(\%results);
};