Do you mean add it like this?
[['country_id'], 'exist', 'skipOnError' => true, 'targetClass' => Country::className(), 'targetAttribute' => ['country_id' => 'id']],
[['sector_id'], 'exist', 'skipOnError' => true, 'targetClass' => Sector::className(), 'targetAttribute' => ['sector_id' => 'id']],
[['type_id'], 'exist', 'skipOnError' => true, 'targetClass' => SecType::className(), 'targetAttribute' => ['type_id' => 'id']],
I tried this and still no cigar.