Попробуйте следующий код:
$subquery = (new \yii\db\Query())
->select(['comp.*', 'TIMESTAMPDIFF(HOUR, comp.created_date, comp.updated_date) AS hours'])
->distinct()
->from('complaints comp')
->innerJoin('complaint_log comp_log', 'comp_log.comp_id = comp.id')
->where(['or',
['like', 'comp.name', $search_name],
['or',
['like', 'comp.id', $search_id],
['like', 'comp.phone_no', $search_phone],
]
])
->andWhere('DATE(comp.created_date) BETWEEN :cStart AND :cEnd', [':cStart' => '2018-01-01', ':cEnd' => '2020-03-20'])
->andWhere(['comp.is_delete' => 0])
->orderBy(['comp.id' => SORT_DESC, 'comp.created_date' => SORT_DESC])
;
$query = (new \yii\db\Query())
->select('cte_name.*')
->from(['cte_name' => $subquery])
->where(['>', 'cte_name.hours', 120])
;