No Mary2e, you do not need to calculate the same credit for New Jersey. New York Form IT-203F shows how much of your current income should be New York versus non-New York income based upon previous employment in New York.
New Jersey residents are taxed on all income received, so the entire payment is taxable to NJ. However, you will only receive an other state tax credit for 60% because 60% is NY income, which is the amount reported on your NY non-resident return. The other 40% would be considered NJ income. A NJ resident would not receive an out of state tax credit on NJ income unless your husband worked in multiple states, in which case you would have to allocate and file other state tax returns.