If he was still living in the same state, then they were already sitting right on his state tax returns, too - and his address must have been written on these. This would be in their very own state taxpayers database.
The state could have done much more than send a couple of certified letters and post a newspaper item. SCOTUS didn't suggest that the state peruse the taxpayer database, but, I'm speculating, was an option available to them.
"There is no reason to suppose that the state will ever be less than fully zealous in its efforts to secure the tax revenue it needs," Chief Justice Roberts wrote. "The same cannot be said for the state's efforts to ensure that its citizens receive property notice before the state takes action against them."