From what you show us, this interpretation sounds correct. Maybe you want to take a closer look at what's currently in %labels by using Data::Dumper:

print Dumper \%labels;
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Also, if you have use strict; at the top of your program (or in the relevant block), that will prevent such bad things as using a string where a reference is expected. If you don't have it, now is a good time to start with the innermost block you're changing and putting use strict; there, just to catch such things.

What's happening is "autovivification" of an array reference.

A quote from the book:
Programming Perl, 3rd Ed., p.251
Chapter 8: References
"Implicit Creation of References"

References of an appropriate type simply spring into existence if you dereference them in an lvalue context that assumes they exist.

So your statement:

    push @{$labels{$tablename}}, $_;
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    $labels{$tablename} = [] if !exists $labels{$tablename};
    push @{$labels{$tablename}}, $_;
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Small nit: It's more like

$labels{$tablename} = [] if !defined $labels{$tablename};
push @{$labels{$tablename}}, $_;
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I stand corrected.
If the $labels{$tablename} already exists but has an undefined value, then that "undef" is replaced with a reference to new anonymous array. I wish this was documented better.

While the OP defines the state of the  %labels hash, it does not say if  $tablename is initialized or not; the signs and symptoms will differ in the two cases (assuming warnings and strictures are used – as they always should be!).

If  $tablename is undefined, it will be 'coerced' to the empty string, which is a valid hash key.

>perl -wMstrict -le
"my %labels;
 my $tablename;
 $_ = 'foo';
 push @{ $labels{$tablename} }, $_;
 use Data::Dumper;
 print Dumper \%labels;
"
Use of uninitialized value $tablename in hash element at ....
$VAR1 = {
          '' => [
                  'foo'
                ]
        };

>perl -wMstrict -le
"my %labels;
 my $tablename = 'bar';
 $_ = 'foo';
 push @{ $labels{$tablename} }, $_;
 use Data::Dumper;
 print Dumper \%labels;
"
$VAR1 = {
          'bar' => [
                     'foo'
                   ]
        };
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You may also find How can I visualize my complex data structure? to be helpful.

Thanks everyone for your replies, esp gmargo. That really clarified the issue. @AnomalousMonk, no $tablename was intialized so that is one thing I didn't have to fight with. :)

Since it is a reference it required appropriate dereferencing to be treated as an array so you can push and pop and do all sorts of array operations on it. This is why @{} is used, it dereferences an array reference.