Yes, you may have to pay the counselling fees and the miscellaneous fees that is needed to fix a seat in IIT's/NIT's. Moreover , AICTE JKPMSS will not help you with the admission process it will be the same as for every other student who is studying without a scholarship.
Moreover, you will get only 1.25 lakhs annum for academic fee and 1 lakh per annum for your maintenance allowance whether you are studying in IIT's/NIT's or a normal engineering college. Amount other than this will that will be required for your studies will be paid by your parents.
Conclusion: AICTE does not provide you extra amount if you are studying in IIT's/NIT's, scholarship amount for all the colleges offering engineering empanelled under AICTE JKPMSSS is the same.