It can be done before or after a workout or at a completely different time.
As you noted some are very effective as part of a warm up/ movement prep.
The mwod is about improving your capacity to be in a good position during movement to improve performance and avoiding injury.
Some are best done following a workout.
Some will depend on what you are doing/ areas you are addressing.
Anything that hits deep would be done after working out or at a completely different time.