"Once both models are constructed, shouldn't the ARIMA values go into the Transfer Function Model Specification?"
You would have to specify the orders of ARIMA for both noise series (i.e., the error term of the output series) and input series like this (See JMP documentation for details.Transfer Functions
Also note that there are a few steps preceding to this final model specification as shown below such as pre-whitening and check cross-correlations, etc.