The Fifth Circuit has determined that TPS holders who travel on advance parole after the commencement of removal proceedings are admitted back into the United States, and therefore, are not arriving aliens. Jurisdiction for their adjustment of status rests solely with the immigration courts (assuming they were not classified as arriving aliens prior to their departure), and if they have a final order of removal, they will first need to reopen their removal proceedings before filing their adjustment of status applications.
The full text of Duarte v. Mayorkas can be found here:
https://www.ca5.uscourts.gov/opinions/pub/18/18-20784-CV0.pdf