This happens because when you do

  $$_ = foo ;
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you are setting to a GLOBAL variable, not lexical (defined by my). So if $_ is equal 'zero' you are setting:

$main::zero = foo ;
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To really set a lexical variable you should use eval:

eval("\$$_ = foo") ;
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Note that when you write

my $zero ;
...
print "$zero" ;
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the $zero variable inside the string to be printed will point to a lexical variable, and all the symbolic references are evaluated at runtime and will point to the package (symbol table), in other words, will point to a global variable.