When you live in one state but work in a different state, your employer is required to withhold state taxes based on the state where you actually work.
The way it works is that at the end of the year you will file a nonresident return with the state of NJ to report only the income you had from that state. You then figure the tax you owe on that income only. You then also file a resident return with the state of DE and report your income from all sources, including your income from the job in NJ. Your DE state tax is then calculated on that total income. DE then allows you a credit for the state taxes you already paid to the other state, thereby reducing what you actually owe to the state of DE.
Since DE tax rates are lower than NJ rates, at this point in time DE will not actually be getting any tax dollars from you on your NJ income. If DE state taxes should increase and become higher than NJ rates, then your DE tax will be calculated based on the higher rates. You will still be given credit for taxes paid to NJ, but may then still end up still owing a small amount to DE if they do increase their rates to be higher than NJ rates.
At this point you do not have to worry about DE charging you a penalty, as you will get credit for all the taxes paid to NJ on your NJ income.
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