It depends.  The underpayment penalty is assessed when you have not paid in enough tax throughout the year.  (The tax system is a pay-as-you-go system, so when you do not pay in enough, you are penalized for not having done so).  However, if you have contributed at least the amount of 2015 tax to this year, you are not assessed the penalty.  That is why the system is asking this question.

However, there is a possibility that there is something else going on.  Delaware does provide a credit for the tax you must pay to NJ for the income you are earning there.  Thus, you want to prepare the NJ return first so that this credit can be applied.  If the credit has been applied and you still owe enough to have a penalty, then you can request your employer to withhold Delaware tax or make estimated payments to not have this situation next year.  My suspicion, however, is that the credit has not been calculated correctly.  Please see this FAQ for more information on how to prepare a nonresident return (to obtain the credit):  https://ttlc.intuit.com/replies/3302052