It depends, but it's probably correct. Both states likely tax you. (But please comment the two states so that we can give further clarification: there may be special circumstances). Your resident state taxes all of your income regardless of where you earned it. Your nonresident state taxes income earned in the state. Your resident state will give you a credit for the amount of tax you must pay to your nonresident state on that double-taxed income, but if the nonresident state has a much lower tax rate than your resident state, then the amount of the tax credit will not cover your resident state's tax liability, and the additional withholding will cover the shortfall.
Having said this, please feel free to comment the states, because there's probably additional detail that I can provide you with that information.
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