Basically, adding the parameter in the prediction query does not retrain your model, or add to your training cases in the mining structure. You must reprocess your model to do that. And, if you have a lot of new data, you probably should retrain your model.
However, if you don't have a lot of new values, EXTEND_MODEL_CASES takes advantage of the formula generated by the model and adjusts the predictions using the new data. You can "back up" the new values into your existing series, or tack them on the end.
Just be careful to get the right start and end points for your predictions.
Take a look at the following tutorial to see how EXTEND_MODEL_CASES works.