@reformedman In the case of NJIT, they publish minimum requirements (GPA and test scores) to be considered for Dorman Honors College. My guess is that most students applying to NJIT that are near or above the ADHC minimums apply for the Honors College as well, probably mostly for the possibility of additional scholarship money. None of the schools where my DD is applying are an “honors or bust” approach to applying, so I think most schools you are considered for Honors College independently of the general admission decision.
Coincidentally, not sure if you know this, but NJIT’s ADHC made at least one ranking as a top 10 honors college:
http://publicuniversityhonors.com/new-top-programs-by-category/
I think Honors Colleges fall into a few camps. I think the best programs (the ones students are most interested in applying for) are ones that offer additional scholarships, special housing, early class registration, and special honors sections of common class requirements. The list goes on with more unusual benefits at some schools. Macaulay Honors of the CUNY schools offers incoming freshman new laptops, for example. Some offer a research or study-abroad stipend.