Start by not using <autotree>. You need to override it 90% of the time (100% in this case), so you might as well make everything explicit.

use strict;
use warnings;

use Data::Dumper      qw( Dumper );
use Parse::RecDescent qw( );

 $::RD_ERRORS = 1; 
 $::RD_WARN   = 1; 
 $::RD_HINT   = 1; 
#$::RD_TRACE  = 1;

my $grammar = <<'_EOGRAMMAR_';
   {
      # These apply to code in those block and all actions.
      use strict;
      use warnings;

      my %escapes = (
         n => "\n",
      );

      sub dequote_double {
         for (my $s = @_ ? $_[0] : $_) {
            s/^"//g;
            s/"$//g;
            s/\\(.)/$escapes{$1} || $1/eg;
            return $_;
         }
      }
   }

   parse    : <skip:'(?:\s+|#[^\n]*\n)*'> portDef(s?) /\Z/
              { $item[2] }

   portDef  : "dbSetCellPortTypes" QSTRING QSTRING portList
              { [ @item[1..4] ] }

   portList : "'" "(" record(s?) ")"
              { $item[3] }

   record   : "(" QSTRING(s?) ")"
              { $item[2] }

   QSTRING  : /"(?:[^"\\]|\\.)*"/
              { dequote_double($item[1]) }

_EOGRAMMAR_

my $parser = Parse::RecDescent->new($grammar)
  or die "Bad grammar\n";

my $text = <<'_EOT_';
dbSetCellPortTypes "/opt/mylib/s956M" "*" '(
  ("gnd!" "Inout" "Ground" )
  ("vint!" "Inout" "Power" )
) #f
_EOT_

my $net = $parser->parse($text)
  or die "bad netlist";

print Dumper $net;
[download]

Other fixes:

• I shortened some rule names. They made it hard to line up the productions.
• It's important to check for end of input (/\Z/).
• Your grammar didn't use strict or warnings, so I added them.
• Properly handled comments using <skip>.
• Changed the format. The one I used makes it easier to locate rules, and makes rule: this | that type rules easy to read. (Just line up the | with the :.)

Update: Fixed portList. (Replaced { $item[2] } with { $item[3] }.)
Update: Fixed comment and missing (s?) in parse.

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