State tax filing

"How does taxes work for that?"
It depends on the details.
1. How long is the assignment expected to last.
2. Does the company pay your bills or give you the money as reimbursement.
3. Will the company add the money to your W-2.

But, the simple answer is: as long as the company doesn’t add it to your W-2, as income; there is nothing you need to do. Your company has an “accountable” expenses plan, per IRS rules, and you taxes aren’t affected.