It is proper for New York to claim more tax than you would owe to Michigan because each state has their own tax system.
The other state tax credit is based on how much tax would be paid if all the income were earned in the resident state, instead of the over state. So, unfortunately, you do get the excess if the other state’s tax is higher. Otherwise you are indirectly getting a credit on other income. For example, if the NY tax is $1,000 and MI tax is $800, if MI gave you a $1,000 tax credit, then the $200 is really reducing tax against other income.
New York is perhaps the most aggressive of all states in taxing telecommuters. It’s generally hard to go against what your employer shows on the W-2.
If you think your employer is incorrect, I suggest filing your return with tax paid to NY. After the return is accepted, you can file an amended state return claiming $0 NY wages and lay out your case. If NY denies your amendment, you owe nothing because you are paid up.
You can also speak with your employer. If your employer is willing to change the withholding to MI you should not have any problem with NY.
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