It can be done either way. What you should do depends on your needs. Usually people want to do whatever is easiest that looks good.
Doing it at runtime, for example using your game toolkit's particle system, allows you to have more dynamic effects.
You can export a frame-by-frame image sequence from other software and put it into Spine. Before 4.1 that is done by putting all the images in a slot, then animating them be showing each one in sequence. In 4.1 you can check the Sequence
checkbox on a region or mesh attachment to do the same more easily.
Using Spine to show the frames has the advantage that you can manipulate the bones they are attached to. For example:
https://www.youtube.com/watch?v=8NWrd1RBi3g
The same YouTuber has many other useful videos, eg:
https://www.youtube.com/watch?v=2MKS8rzKp-Y