CakePHP2 with custom finder & Auth condition on pagination

Need Help
1

In an app that uses CakePHP 2.9.2, I have the goal of using custom finders along with pagination with a condition.

First point: I need to filter the records based on a condition related to the business logic. So, I understand that the correct way to do this is creating a custom finder. Note that the condition involves two models: Alfa & Beta.

class Alfa extends AppModel
}
    // (...)
    protected function _findWithoutPending($state, $query, $results = array())
    {
        if ($state === 'before') {
            $query = array_merge($query, array(
                'conditions' => array(
                    array(
                        'NOT' => array(
                            'Beta.done' => null
                        )
                    )
                )
            ));
        
        $query['joins'] = array(
            array(
                'alias' => 'Beta',
                'table' => 'betas',
                'type' => 'LEFT',
                'conditions' => 'Alfa.id = Beta.alfa_id'
            )
        );
        
        return $query;
    }
    
    return $results;
}

Second point: I want to only retrieve records from the logged in user. Because the login info is on the Controller layer, I understand that this condition must be passed to PaginatorComponent. So, in the Controller, I do:

// Apply filter from a custom finder
$this->paginate = array(
    'findType' => 'withoutPending'
);

// Retrieve only records from the logged in user
$this->Paginator->settings = array(
    $this->modelClass => array(
        'conditions' => array(
            $this->modelClass . '.user_id' => (int) $this->Auth->user('id')
        )
    )
);

// Paginate
$alfas = $this->paginate();
$this->set(compact('alfas'));

The issue is that with this code, Cake is only filtering by the Auth criteria:

WHERE `Alfa `.`user_id` = 4 ORDER BY //...

And, just removing the $this->Paginator->settings block, then Cake applies this condition:

WHERE NOT (`Beta `.`done` IS NULL) ORDER BY //...

I want this query:

WHERE `Alfa `.`user_id` = 4
AND NOT (`Beta `.`done` IS NULL)
ORDER BY //...

How can I achieve this with CakePHP2?

Thank you very much.