There are several different issues here -- unlawful presence bans, and eligibility for Adjustment of Status.
An individual received DACA several years after turning 18, so so they have accrued unlawful presence and are considered inadmissible.
Assuming they entered illegally, or they entered legally on an I-94 that had a definite end date, they have accrued unlawful presence, but they are not (yet) inadmissible. In order to trigger a 3-year/10-year ban under INA 212(a)(9)(B), the person must accrue 180 days/1 year of unlawful presence and then leave the US. This person has not left the US since they accrued their unlawful presence, except through the TPS travel authorization. The BIA ruled in Matter of Arrabally (2012) that if someone departs based on a grant of Advance Parole and returns on that Advance Parole and is paroled in, it does not count as a departure for the purposes of INA 212(a)(9)(B), and thus does not trigger the unlawful presence ban even if the person has years of unlawful presence. Now, the person in this case received an I-512T, a TPS travel authorization, which is not exactly the same as Advance Parole (they used to issue Advance Parole to TPS beneficiaries, but switched to a separate I-512T for TPS due to certain court rulings), but the exact same reasoning of Arrabally should apply to I-512T. Since they do not have the ban, they do not need a waiver for this ban (at least not unless they need to leave the US, triggering the ban).
But just because they don't have a ban doesn't mean they can do Adjustment of Status. The entry on Advance Parole or on TPS-based travel authorization satisfies the "admitted or paroled" requirement of Adjustment of Status. But there is another requirement of Adjustment of Status that applies to people in most categories outside the Immediate Relative category (spouse, parent, or unmarried under-21 child of US citizen) -- they must have never been out of status, on the current or a previous stay. This subsection clearly states that departure does not erase this ineligibility, so this person's having been out of status on their previous stay would render them ineligible for Adjustment of Status.
This is why DACA-based Advance Parole and TPS-based travel authorization are Adjustment of Status loopholes mainly for people in the Immediate Relative category -- because the Immediate Relative category AOS only cares about being admitted or paroled, and does not care about having been out of status. (Note: Entry on Advance Parole or I-512T never "cures" unlawful presence -- but it doesn't need to, as unlawful presence does not by itself cause a ban, if the person has not left the US (other than on Advance Parole or I-512T). The main purpose of leaving and returning on Advance Parole or I-512T is to satisfy the "admitted or paroled" requirement of Adjustment of Status for someone who entered illegally.)
So normally, someone in a non-Immediate-Relative category like the person described here, would not be able to do Adjustment of Status due to having been out of status during their previous stay, even if they left and returned on Advance Parole. They would thus need to do Consular Processing abroad. But leaving the US would trigger the unlawful presence ban, for which they would need a waiver. They could apply for the waiver with I-601 while abroad and applying for the immigrant visa at the consulate, or they can apply for a provisional waiver with I-601A, and get the results, before they leave the US. When they leave the US (thus triggering the ban), and go to the consulate to get the immigrant visa, the provisional waiver gets turned into an actual waiver, and they get the immigrant visa without needing to wait long outside the US.
But there is an additional wrinkle in this case, because they are immigrating in an employment-based category. AOS in employment-based categories (EB1, EB2, and EB3) can benefit from INA 245(k), which means they are exempt from the ineligibility for AOS due to having been out of status or unauthorized employment, if they have been out of status or working illegally for less than 180 days since their most recent admission. Normally, departure and return on Advance Parole doesn't help with this, since this rule specifically says "admission", and parole is not an admission, so they would still consider the out-of-status days from the previous stay before they left on Advance Parole, which in this person's case is more than 180 days. But in this case, the person left and returned on I-512T, the TPS travel authorization, and one of the differences between Advance Parole and I-512T is that someone returning on I-512T is "admitted", not "paroled", into TPS status. So perhaps, this return on I-512T does "reset" the out-of-status days for the purposes of INA 245(k), which would mean they can do Adjustment of Status in an employment-based category after all.
I haven't seen any official sources regarding the interaction between TPS travel authorization and INA 245(k), so I cannot confidently say that this will work.