You should trim your code down to a minimum (you are improving) and make it stand alone so that we can reproduce your problem.

if ($j == 0) is always false because your loop starts with $j = 1.

If I edit your code to this:

use warnings;
use strict;
use Spreadsheet::WriteExcel;

my @model = qw(x a b c d);
my @devicesPerVariant = qw(x 2 1 3 1);
my $rowCounter = 1;
my $devicePerModel = 2;

my $workbook = Spreadsheet::WriteExcel->new("test.xls");
my $worksheet = $workbook->add_worksheet();
my $j = 1;

#Declare Headings for row 0 and the 6 Columns
$worksheet->write(0,0 , 'Equipment Model');
$worksheet->write(0,1, 'Devices Per Model');

#Loop through Global Array called Models to determine the number of ro
+ws to place data
for (my $j = 1; $j <= $#model; $j++)  {
  print "row is $rowCounter, $model[$j], $devicesPerVariant[$j]\n";
  $worksheet->write($rowCounter,0, $model[$j]);
  if ($j == 0) {
    $worksheet->write($rowCounter,1, $devicePerModel);
  }
  
  $worksheet->write($rowCounter,2, $devicesPerVariant[$j]);
  $rowCounter++;
  }
$workbook->close();
[download]

I get a spreedsheet containing:

Equipment Model Devices Per Model    
a               2
b               1
c               3
d               1
[download]

which is what I would expect to get.