Generally - the state tax liability is based on either residency or job location.
Emplyers are required to withhold state income taxes based on the job location.
In your situation - because your husband is working in several states - his employer is required to account for the time spent in each state and withhold state income taxes accordingly.
It seems as his employer is trying to avoid overhead for accounting for his working time and simply will report all his working time as being working in SD.
That doesn't eliminate your husband's responsibility to report his income to Minnesota. According to state income tax regulations - he will be non-resident of Minnesota and will be taxed only on income from sources in that state.
If Minnesota DOR later finds out about unreported income - taxes and penalties will be assessed to your husband and his employer.
Sorry if that is not the answer you've expected. Please let me know if you need any help or clarification.
How would the MN DOR find out about unreported income, if his company pays him based on all his working time being worked in SD?
We may not know if Minnesota DOR will or will not find out about unreported income. It is possible that they will never find out. But on the other hand - all states nowadays are short on revenue - and are hard on their collection efforts. We may not say that they will never find.
Thank you for all this information. Very much appreciated.