I’m also interested in solving this problem (I think the number 1 is actually the user id). The only way I could find is to use bp_before_activity_add_parse_args filter:
function me_activity_parse_filter( $cpt ) {
    if ( $cpt['type'] == 'your_custom_type' ) {
        $cpt['item_id'] = bp_get_current_group_id();
    }     
    return $cpt;
}
add_filter('bp_before_activity_add_parse_args', 'me_activity_parse_filter');
However, if the cpt post is updated a new activity is created instead updating the original one…
Note that in bp_activity_set_post_type_tracking_args I have
'component_id'	=> 'groups',
Maybe  @imath can help us to solve this issue.
		
	 
	
	
	
 
		
			
	
	
		
		Here is another approach. I dont like it at all because you cannot check a custom post type (you dont have the activity object). But it works.
function me_filter_bp_activity_item_id_before_save( $item_id ) { 
    if ( !empty(bp_get_current_group_id()) ) $item_id = bp_get_current_group_id();
    return $item_id ; 
}; 
         
add_filter( 'bp_activity_item_id_before_save', 'me_filter_bp_activity_item_id_before_save', 10, 1 );
BTW: The value 1 seems to be the default blog ID.
In this thread  @imath explains that:
Custom Post Type Support for Activity
		
	 
	
	
	
 
		
			
	
	
		
		I found a workaround to avoid the creation of duplicate activities for the same cpt post on updating.
function me_activity_parse_args_filter( $args = array() ) {     
    if ( !empty( $args['type'] ) && $args['type'] == 'new_your-cpt' ) {
                $activities = bp_activity_get(array(
                        'max' => 1,
                        'filter' => array(
                        'action' => 'new_your-cpt',
                        'secondary_id' =>  $args['secondary_item_id'],
                        ),
                ) );
                if (count($activities['activities'])==0) { // The cpt post doesn't have activity yet, so we set the group information
                        $args['component'] = 'groups'; // You could set this as 'component_id' in bp_activity_set_post_type_tracking_args
                        if ( !empty(bp_get_current_group_id()) ) $args['item_id'] = bp_get_current_group_id();
                        if (empty($args['content'])) $args['content'] = ' ';  // To make sure content filter applies afterwards 
                } else { // Activity already exists
                        $args['type'] = false; // Delete duplicate activity
                }
    }     
    return $args;
}
add_filter('bp_after_activity_add_parse_args', 'me_activity_parse_args_filter',10,1);