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}}, $_;
is the same as:
$labels{$tablename} = [] if !exists $labels{$tablename};
push @{$labels{$tablename}}, $_;
See also
autovivification in the glossary, and
perlref.
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