@Loro It sounds like the NJ construction site would be a New Jersey workday. He is there out of his employer's necessity and not his own convenience, and while its not a "bona fide" office of his employer persay, characteristically its similar. You likely should not have paid NYS taxes in these years. However, NJ and NYS have a very similar tax rate and its likely you got a credit in NJ for taxes paid to NY. If you are ever audited by NJ, you should upon receiving that notice file an amended return in NYS to protect your right to claim a refund for any potential taxes you may owe to NJ.
Regarding unemployment, its different than personal income tax. From my limited understanding I believe its based on physical presence, so his employer should have been paying that in NJ where he was primarily working.
Kristine L. Bly, EA Private Client Services / Residency / Tax Controversy
Partner, Cohen & Company
