It depends. The few states that have no income tax, obviously, won't tax your income.

Most states with an income tax will try to tax your income if it originates in their state. From personal experience as someone who has lived in Washington State (no income tax) and worked in Oregon (income tax up the wazoo), if the work is done "in Oregon" you are taxed.

But, and this was especially true during the pandemic and everyone working remotely, if you're not in the state, and the employer isn't based in Oregon (i.e., headquartered out east somewhere), and you don't reside in Oregon, you don't owe Oregon tax for any work not done in the state. Most employers will deduct taxes for Oregon as if you worked there all year. Just keep a spreadsheet full of days worked vs not worked in Oregon, and fill in the right box on the OR-40-N. They'll send you a letter asking for a signed letterhead from your employer supporting your math, so, if you're no longer with that employer, get that before you quit / part ways.

Oregon/Washington is like this. As far as I know, if you live in WA but work in Oregon, you pay a reduced non resident tax rate to Oregon. You're still using the public resources that taxes cover such as roads.

I know for California working in California means you’re subject to California income tax for that work.

Most states tax you according to where you live, not where you work. Several exceptions exist, though. One notable exception is New York State, which will tax you if your employer is based there, even if you don't live there, unless it can be demonstrated that the employer needs you to live outside the state to do your job. (Google "NY convenience of the employer" for more info on that.)

I would talk with your HR department. It's possible that they determined you are responsible for taxes in both states, and misfiled the paperwork.

You need to look this up specifically for the states involved. It varies. Some neighboring states have reciprocity agreements if they have a major city near a shared border. Frequently what happens is you'll have to file in both states, but one will give you a non-refundable credit for the tax amount paid in the other.

I suspect that in your situation you'll end up having to pay the full amount of income tax of the state your employer is in.

Whether that's legal: states get to do whatever they want to collect taxes.

https://www.cnn.com/2022/03/01/success/state-income-tax-ramifications-remote-work/index.html

Generally speaking you are taxed/follow employment laws of the state you do the work in.