You have selected a model for the response in one experiment. The results in the Pediction Profiler are now based on the model, not the data. That is, the behavior of the profiles won’t change unless the model changes. Using the model with new data (I.e., the second experiment) will produce the same profiles.
What do you mean by, “the factors of the new experiment don’t exactly align to that of the DOE?”
If you mean by “to the exclusion of the processing step” that some of the original DOE factors were not varied but held at a fixed level? You can simply add data columns for those fixed factors and populate them with the given level. You could also replace the exluded factor column in the formula with the fixed level.