I rewrote a bit to get to work on command line with manually entered input:

use warnings;
use strict;
use File::Basename;
use Data::Dumper; 

my %file_data;
my @field_headers = ();

open(OUT, ">inbound.txt")    || die("can't open output file: $!");

# read all of the files dropped onto the batch file
while (<>) {

      if(!m/^quit$/)
      {
    #grab and save the column headers on the first line
    if($. == 1) {
        #@field_headers = @{split_csv_string($_)} ;
                @field_headers = split_csv_string($_) ;
    # read the rest of the lines. each 'record' is a hash with the
    # field name as the key. each 'record' is added to the array of
    # records for that file
    } else {
        my %record;
        my $i = 0;

        foreach my $field_val ( split_csv_string($_) ) {
            $record{ $field_headers[$i] } = $field_val;
            $i++;
        }
        # ****** $file_data IS OK HERE!  ******
        push @{ $file_data{ $ARGV } }, \%record;
    }    

    # reset line numbering on each input file
       }
       else
       {
        
        close(ARGV);
        @field_headers = ();
    }
}

sub split_csv_string {
  my ($str) = @_;
  chop($str);
  return split q|,|,$str;
}

print Dumper %file_data;
[download]

When I manually enter a,b,c ; 1,2,3 ; 4,5,6 (where ';' is actually an CRLF) I get:

$VAR1 = '-';
$VAR2 = [
          {
            'c' => '3',
            'a' => '1',
            'b' => '2'
          },
          {
            'c' => '6',
            'a' => '4',
            'b' => '5'
          }
        ];
[download]

I realize this output would probably look different run in your environment and the way you are running your code. You can open a filehandle for diagnostic output, run it in your environment, and see what you get and operate from there. I would personally recommend that you rewrite this code entirely and use Text::CSV in a way that you can easily debug when needed.