State tax filing

@mackenzze --

Since your employer is based in New York, and since you perform your work both within and without the State of New York, your work income is subject to New York's "convenience of the employer" doctrine.  Here is NY's rule:

"However, any allowance claimed for days worked outside New York State must be based upon the performance of services which of necessity, as distinguished from convenience, obligate the employee to out-of-state duties in the service of his employer."

https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf

By your own statement, the work you do in Michigan is done there for your own convenience.  The convenience rule means that, for tax purposes, New York will treat the days you worked in Michigan as if they were days worked in New York.  That means, even though you physically work in New York only 10% of the time, ALL your work income is taxable by New York.  It is also taxable by Michigan, since Michigan residents are taxed by Michigan on their entire income, regardless of its source.

You will be able to claim an "other state credit" on your Michigan tax return for the taxes paid to New York on the dollars taxed by both states, so in effect you won't be double-taxed.

With TurboTax, be sure to complete your non-resident NY tax return before you do your home state MI return, so that the program can correctly calculate and apply the credit.   Finally, be sure your employer withholds NY taxes from your pay.