How does this work? Is it based on your domicile, or where you actually reside?

Since normal people pay taxes in the state they live in, go with that.

Where you reside.

It's based on where you reside. But you must ensure that you fill out the appropriate state income tax form when you apply. If not, they will deduct MN taxes, and you will have to file two state tax returns (unless you live in a tax-free state).

FL and TX, both income tax free states!

Some places require workers in their state to pay income tax whether they live there or not.

Two of the seven you listed. Here's all of 'em:
Alaska, Florida, Nevada, South Dakota, Texas, Washington, and Wyoming.

Also, don't forget that most states that don't charge income tax charge a lot higher real estate tax. Alaska, Texas, and Florida come to mind.

Fight this, if you can. Attempt to only pay taxes in your resident state. Otherwise, you will have to file a non-resident tax return where you paid taxes, and a resident return in your home state. Also note - if your home state and the non-resident state where you paid taxes do not have a reciprocal agreement, you MAY end up paying more taxes than you would if you paid only resident state taxes. Research is your best friend.

Good luck fighting the Socialist State of California Franchise Tax Board. You WILL pay California state income tax, regardless of which state you reside.

Only if your income was earned in California.