If you visualize in Template space, the electrodes are registered to the atlas (which remains the same model), if you visualize in native space, it is the other way around (and that is sometimes called “atlas based segmentation”). So in both steps the patient data is used. However, in the template visualization, the atlas does not change at all. This is crucial for group studies, i.e. to make electrode placement comparable across patients.
I can recommend for you to read the newest Lead-DBS methods paper for some more info: https://www.researchgate.net/publication/327380509_Lead-DBS_v2_Towards_a_comprehensive_pipeline_for_deep_brain_stimulation_imaging
It is easily written and gives a good overview about what Lead-DBS does.