Clarifying what it means to be Strongly NP-Complete
Yes, that's correct.  You'll probably have to figure out the polynomial yourself.  The way to find the polynomial is to look at the reduction, and from that you should be able to deduce a polynomial.

In your case, I believe there is a reduction from 3D-MATCHING to 3PARTITION, so you would analyze that reduction to find the polynomial.  Given an instance of 3D-MATCHING, the reduction explicitly constructs an instance of 3PARTITION whose solution can be used to solve the 3D-MATCHING instance; so you'd analyze how large the parameter of 3PARTITION instance could possibly be, as a function of the size of the set, and that would tell you the polynomial $p$ you are looking for.