Programmically add Product to Product Display (Profile)

Question

I am trying to use a rule to add a product to a profile. Also, I am using an autocomplete entity reference widget for the product reference field.

Currently I can see the product being added but not saved/updated.

If I dpm() the profile at the end of the function I can see that the product is being added correctly, but when I review the profile it is not there.

Here is the rule I have created:

function mymodule_add_product_rule ($account,$sku){ 
  $uid = $account->uid;
  $product = commerce_product_load_by_sku($sku);
  $product_id = (string)$product->product_id;
  $profile = profile2_load_by_user($account, 'profile_machine_name');
  $wrapper = entity_metadata_wrapper('profile2', $profile);
  $wrapper->field_product->set($product_id);
  //dpm($profile);
}