It depends.
If you anticipate owing more than $500 in Wisconsin, then you would have to make estimated tax payments. But based upon your research, you would qualify under the special withholding and would only need to have income taxes withheld in Minnesota. You would be able to claim a credit on your resident Wisconsin tax return for the income taxed in Minnesota.
You should qualify as a Wisconsin resident working in Minnesota as you appear to meet the requirements.
Please see the link below for additional information on your filing requirement in Minnesota.
Minnesota filing requirement
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