This line is your problem  

    $this->getCollection()->load();

You are loading the collection and later you apply a filter in the template.  
Once you load the collection all filters and sort orders applied have no effect.  
So you should apply the filter before calling `load` or before iterating through the collection.  
In this case you should apply the filter in the block class.  

As a general case, the templates should be used only to present data, so all data manipulation should be done in the block classes.

**[EDIT]**  
Make your construct method look like this:

    public function __construct()
    {
        parent::__construct();
        $collection = Mage::getModel('module/model')->getCollection();
        $customerId = 1;
        $collection->addCustomFilter($customerId);
        $this->setCollection($collection);
    }