You can not dereference a string "HASH(0x1a031f4)" because it is not a reference. Your $array is a reference to an object HTML::Element, so use it's methods

while(my ($key, $value) = each(%{$tree})) {
        if (ref($value) eq 'ARRAY')  {
             foreach my $array (@{$value}) {
               for (@{  $array->extract_links('a', 'img')  }) {
                  my($link, $element, $attr, $tag) = @$_;
                  print
                       "Hey, there's a $tag that links to ",
                       $link, ", in its $attr attribute, at  ",
                       $element->address(), ".\n";
               }
             }
        }
}
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see HTML::Element

Update: misprints fixed