As soon as you start working on German soil, German employment laws apply fully. Citizenship, prior residence, etc. are almost completely irrelevant. There is a social security agreement between the US and Germany which might exempt the person from German pension contributions but nothing more.
(If the spouse is working for the US military there are NATO agreements which might make German employment law inapplicable but I know almost nothing about that.)
(If the spouse is working for the US military there are NATO agreements which might make German employment law inapplicable but I know almost nothing about that.)