Nested query filter not being applied

I'm using the api to pull out a few contacts that meet a particular criteria and their associated activites. So I'm using the api's chained syntax that looks like this:

$results = civicrm_api('contact', 'get', array(
'version' => 3,
'contact_type' => 'Organization',
'contact_sub_type' => 'Party',
'world_region' => 1,
'options' => array(
'limit' => 20,
),
'api.activity.get' => array(
'source_contact_id' => '$value.id',
'activity_type_id' => '54',
),
));

You can see that I'm trying to filter the associated activities based on two criteria: activity_type_id and source_contact_id. However, neither of these filters appear to be applied.

Is this not expected to work, or is it a bug?