The seeing of past lives by the Buddhas is supposed to be part of an insight into selflessness, of the three marks and four truths, etc., not selfhood. The Buddha doesn't see himself in the past and conclude that it is seen that the same consciousness transmigrates successively. In contrast, in DN 1, many different cases of the seeing of past lives are described and, in some way, are described as incomplete ("they recollect that past life, but no further," DN 1). In the case of mendicants who have visions of themselves as Brahma arise during their meditation, in DN 1 this leads to self-views and eternalism, partial eternalism, etc., ultimately leading to ensnarement in a "net of Brahma," the titular net of the sutta, that is comprised of a thicket of views.
So it has to be concluded that these seeings of past lives in DN 1 are in a fundamental way unlike the Buddha's seeing of past lives, which is associated with awakening, insight into the 4 noble truths, selflessness, etc. The obvious answer right in the text is that the seeings of the DN 1 speculators are "tato paraṃ nānussarati" -- and someone can start a thread in the Pali subforum if they want a more precise breakdown than how Ven Sujato rendered it in the earlier translation. I certainly can't. The Pali lookup dictionary at SuttaCentral suggests maybe something like "(but) thereafter, he doesn't remember," but that is a guess. The Buddha's seeing of past lives is clearly different than these seeings, where meditators suddenly envision themselves as avatars of a former God-Self, and the reason suggested in the text is that the Buddha's recollection/seeing is "further," presumably to an extreme degree. The Buddha's recollection of past lives is associated with his viewing the dharmas are selfless, the samskaras are suffering and impermanent, not associated with realization of himself as Brahma, eternal etc., like in case of the mendicants in DN 1.
The Buddha, from within his seat of samādhi, emitted a great circle of light from his head, casting luminous prajñā towards Mañjuśrī and the eighty-four thousand monks. A sword of wisdom appeared from the top of Mañjuśrī's head, and from his side emerged a golden-haired lion. [...] The Tathāgata spoke:
The supreme path of all Buddhas
is marked by perfect luminosity and eternal dwelling.
Those who enter the dhyāna samādhis together with the Buddhas,
in the same way as they, realize bodhicitta.
(Nihon Daizōkyō Hensankai, Shugendō Shōso 1, Bussetsusanjinjuryōmuhenkyō, excerpts)