So, the question, as I mentioned above and as you saw in the sub, how does the subroutine know it's container hash key, in order to calculate the right key's qty values?

Various ways.

• with closures. Don't stuff a reference to qtyTotal() into the "qtyTotal" slot, but a subroutine which calls qtyTotal with the right argument. The argument could be either
  1. the key for that container:

     my %phrases = (
      "phrase 1" => {
        qty        => 1,
        qtySum     => 5,
        qtyCont    => 8,
      },
      "phrase 2" => {
        qty        =>10,
        qtyCont    =>34,
      },
      "phrase 3" => {
        qty        =>1,
      },
     );
     
     for my $k (keys %phrases) {
      # update
      # $phrases{$_}->{ qtyTotal} = sub { qtyTotal($_) }
      $phrases{$k}->{ qtyTotal} = sub { qtyTotal($k) }
     }
     
     sub qtyTotal{
      my $qty = 0;
      my $key = shift;
      my $phObj = $phrases{$key};
      foreach my $qType ('qty', 'qtySum', 'qtyCont'){
       $qty += $phObj->{$qType} if exists $phObj->{$qType};
      }
      return $qty;
     }
     [download]

  2. the container itself (better):

     for my $k (keys %phrases) {
      # update
      # my $ref = $phrases{$_};
      my $ref = $phrases{$k};
      $ref->{ qtyTotal} = sub { qtyTotal($ref) }
     }
     
     sub qtyTotal{
      my $qty = 0;
      my $phObj = shift;
      foreach my $qType ('qty', 'qtySum', 'qtyCont'){
       $qty += $phObj->{$qType} if exists $phObj->{$qType};
      }
      return $qty;
     }
     [download]

     That way the subroutine qtyTotal() doesn't need to know about %phrases and could be in a different scope. And you could e.g. have "aliases" in your %phrases hash, saying $phrases{"phrase 4"} = $phrases{"phrase 2"}.
  
  In either case, you need the reference/dereference trick to interpolate the results of a subroutine call into a double-quoted string:

  print "${ \$phrases{'phrase 2'}->{'qtyTotal'}->() }\n";
  [download]

• make the containers into objects, so they "know themselves" (best):

  package Qty;
  sub new {
      my $class = shift;
      bless { @_ }, $class;
  }
  sub qtyTotal {
      my $phObj = shift;
      foreach my $qType ('qty', 'qtySum', 'qtyCont'){
          $qty += $phObj->{$qType} if exists $phObj->{$qType};
      }
      return $qty;
  }
  
  package main;
  
  my %phrases = (
   "phrase 1" => Qty->new(
     qty        => 1,
     qtySum     => 5,
     qtyCont    => 8,
   ),
   "phrase 2" => Qty->new(
     qty        =>10,
     qtyCont    =>34,
   ),
   "phrase 3" => Qty->new(
     qty        =>1,
   ),
  );
  
  print "${ \$phrases{'phrase 2'}->qtyTotal() }\n";
  [download]

  This approach has the advantage that you can add more methods (e.g. qtyAverage()) to the Qty class and use them without having to change the way in which you populate %phrases.

As a rule of thumb - if you ask yourself how does X know it's Y, the object approach suits best.

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