Perl Regex 'e' (eval) modifier with s///

I'm having a little trouble comprehending this simple use of the /e regex modifier.

my $var = 'testing';
$_ = 'In this string we are $var the "e" modifier.';

s/(\$\w+)/$1/ee;

print;

Returns: "In this string we are testing the "e" modifier."

I cannot see why two 'e' modifiers are required. As far as I can see, $1 should capture '$var' from the string and a single 'e' modifier should then be able to replace the variable with its value. I must be misunderstanding something however, since trying the above code with just one 'e' modifier does not visibly replace anything in the string.

Excuse me for asking such a simple question!

Thanks.