This question gets asked periodically.
In a workout mixing multiple kinds of lifts, we try to do those with the highest level of skill first. Thus, explosive lifting before grinds, and grinds before cardio.
In the original Program Minimum from ETK, the getup was a grind and the swing was cardio, hence getups first. In Simple & Sinister, the swing is an explosive lift and the getup still a grind, hence swings first. The S&S swing is designed to use different energy systems, from what I understand. Certainly the priority is on being maximally explosive, and if that is the priority, then it has to come first in a workout.
-S-