If I owed taxes in another state, did my current state already balance the debt to compensate owed amount, so I owe nothing?

Negative.

You must APPLY for the tax credit for taxes paid to another state when you file your current state tax return. This credit applies only if you worked and paid taxes to another state while living in your current state.

If you worked and lived in another state, then moved to your current state to work and live, then you will file part-year returns in each state, paying taxes only on income earned in each respective state.