In the first diagram (straight sandwich core), the value of NLOC doesn’t change the fact that the applied loads are at the node points. When NLOC is nonzero, the cross-section center is offset from nodes so it would seem reasonable that the section is no longer in pure tension. On the other hand, if the load were transverse to the straight member so as to produce flexure, it would make sense to me if NLOC had no effect.
Having the input data would be helpful in addressing this matter more thoroughly, but we cannot accept input files via the forum. You may share files if you submit a support case to https://customer.ansys.com and assign the task to “NA Structures”. If you choose to do that, please run both of your experiments using the explicit solver and again using the implicit solver, and note any differences in the effect of NLOC using these two solvers. Thanks!