نعم أطلقوا القول بحدوث ما سوى الله تعالى
Yes, they also used the term origination for what is other than God Most High.
Shared use of the word ḥādith does not guarantee agreement in doctrine. One writer may mean existence after nonexistence, while another means dependence on another for existence. The expression is shared but the concept is not.
One must therefore compare the defined claims, not merely the vocabulary. A position that denies a temporal beginning is not identical to the theologians' position just because both use the word 'origination'.