OK, so there are many problems with your code… But I’m pretty sure I know, where the major one lies…
But first things first…
You add your AJAX callbacks with this code:
add_action( 'wp_ajax_wilcity_handle_review_listing', 'address_save_postdata' );
add_action( 'wp_ajax_wilcity_handle_review_listing', 'address_save_postdata' );
It doesn’t make sense to add the same function twice. It can be a mistake, but maybe you forgot to add nopriv to the second line.
And back to main problem…
There are arrays sent in the POST request and you’re trying to access them like so:
$_POST['data[tmbu_location][group][tmbu_lng]']
It won’t work. 'data[tmbu_location][group][tmbu_lng] is not a string key. It’s an array with three keys. It means, that you should access it like so:
$_POST['data']['tmbu_location']['group']['tmbu_lng']
PS. And one more thing. You’ve put esc_attr everywhere in your code. But it doesn’t make much sense, I’m afraid. esc_attr is a function that does the escaping for HTML attributes. You don’t print any html attributes anywhere in your code. You don’t have to escape string before comparing them or saving them to DB and in most case you shouldn’t do so.