I believe he traced it back to the Prophet ﷺ, who said that when he raised his head from bowing, he would say, "Allah hears the one who praises Him. O Allah, our Lord, to You belongs all praise, filling the heavens, filling the earth, and filling whatever else You will beyond that."
حدثنا سريج حدثنا حماد يعني ابن سلمة عن قيس بن سعد عن سعيد بن جبير
أحسبه رفعه قال كان إذا رفع رأسه من الركوع قال سمع الله لمن حمده اللهم ربنا لك الحمد ملء السماء وملء الأرض وملء ما شئت من شيء بعد
Its isnad is sahih. It appears that the one who was uncertain about attributing it directly to the Prophet was Hammad bin Salama, for Muslim (1:137-138) narrated it both at length and in brief, and Nasai (1:162) narrated it in brief, both via Hisham bin Hassan, from Qays bin Saad, from Ataa, from Ibn Abbas, attributed directly to the Prophet without any doubt. It is possible that Ataa was the one who affirmed it decisively as attributed to the Prophet, while Saeed bin Jubayr was the one who had doubts about it. In any case, it is a sahih hadith.