while (<INPUT>) {
   ($userName,$emailAddress,$division,$fullName)  = split(/\|/, $_);
    while (@lines) {
     my $pattern = pop @lines;
     $pattern=~s/\n//g;
     if ($emailAddress =~ /$pattern/) {
      print $pattern . "  exists in " . $emailAddress."\n";
     } else {
      print $pattern . "  no match  " . $emailAddress."\n";
      last;
     }
   }
[download]

should be

  my $exists = 0;
  while (<INPUT>) {
   ($userName,$emailAddress,$division,$fullName)  = split(/\|/, $_);
    while (@lines) {
     my $pattern = pop @lines;
     $pattern=~s/\n//g;
     if ($emailAddress =~ /$pattern/) {
      $exists = 1;
      last;
     }
   }

   if ($exists) {
    print "$emailAddress exists\n";
   } else {
    print "$emailAddress doesn't exist"\n";
   }
[download]

because you only want to print if it doesn't exist after you've checked all of the patterns, not just the first.

A hash would be make more sense, though.

sub main {
  my $input_qfn   = "input.file";
  my $pattern_qfn = "pattern.file";

  my %patterns;
  {
    open(my $pattern_fh, '<', $pattern_qfn)
      or die("Can't open pattern file \"$pattern_qfn\": $!\n");

    while (<$pattern_fh>) {
      chomp;
      ++$patterns{$_};
    }
  }

  open(my $input_fh, '<', $input_qfn)
    or die("Can't open input file \"$input_qfn\": $!\n");

  while (<$input_fh>) {
    chomp;
    my ($userName, $emailAddress, $division, $fullName) = split /\|/;
    if ($patterns{$emailAddress}) {
      print "$emailAddress exists in the pattern file\n";
    } else {
      print "$emailAddress doesn't exist in the pattern file\n";
    }
  }
}
[download]

Output:

David@domain.com exists in the pattern file
Cory@domain.com doesn't exist in the pattern file
Tania@domain.com exists in the pattern file
Geoffrey@domain.com doesn't exist in the pattern file
[download]

(Most people use four space indentations. One space is just not enough. You couldn't even tell that the indentations didn't line up correctly! As such, I doubled your indentation in my suggested solution.)