Timing particles for animation: Where to begin?

Good day, everyone!

Recently I have been testing and learning about how to configure and use the particles systems and emisors within Unity. Also, I have begining to animate sprites and little 3D Characters through the animator and state machine for give a little bit of "soul".

But when I try to use more complex particle systems, those with 6 or 8 different emissors, it seems that they just play inmediatly all together (I know that I can make them play / stop by scripting, but that's not the point). My doubt is: Which is the best way to animate the different emissors within a complex particle system, and time them correctly for either characters with state machine or world itself?

In case I'm not explaining myself, something like these examples, where the different emissors seem to be timed to their exact moment: https://www.youtube.com/watch?v=god-YAz2eU4