You pay tax in both states. The income you earn in each state is taxed by that state. It doesn't matter whether it's on the same day or different days. The payment of tax is determined by where you earned the income, not day by day. If you work in two states in one day, you pay tax to both states, on the income that you earned in each state.
All your income is taxed by the state that you live in, no matter where you earn it. In most cases your tax return for the state that you live in will give you a credit for tax that you pay to other states. To be able to give you more specific information, we would need to know the particular states involved, and which state you live in.
