The state in which a taxpayer is a resident normally taxes all income from any state. If taxes are paid (not just withheld, but paid on a state tax return) to another state, the home state typically allows a credit on its return for taxes paid to another state. There are some exceptions; for example, some states have reciprocal agreements so that their residents don't have to file a return in the other state. Also, Arizona doesn't tax the Arizona income of California residents that will be taxed on the California return.
The employer correctly shows all earnings as potentially taxable by both states. In the Federal section of TurboTax, indicate that she is a resident of your home state and earned income in another state.
When you live in one state and work in another, you often need to prepare two state tax returns - a nonresident return for the state in which you work and a resident return for the state in which you live. In this situation, you generally prepare the nonresident state return first. Follow the prompts in the nonresident state return in TurboTax to identify which income from your Federal return is sourced in that state. If there is tax due to that state, you may be able to claim a credit on your resident state return for the tax paid to the other state.
Some states have reciprocity agreements so that you don't have to prepare two returns if you only receive wages in the nonresident state.
See this article for information on states with reciprocity agreements.
See also this TurboTax article and this one on multiple-state situations.
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