I don’t anticipate much effect from this. Non-citizen voting barely occurs (confirmed cases measure in the hundreds). The bigger issue if people are illegitimately flagged as non-citizens. That said, I would expect provisional ballots and counties to be the arbiters.
BREAKING: The Supreme Court allowed the Trump administration to resume its expanded voter citizenship verification program, which lets states use Social Security records to check voters' citizenship. Justices Sotomayor, Kagan, and Jackson dissented.