I’m at work so I can’t open the youtube link to be certain of what you want, but a few options come to mind.
You could use larger particles with scale size over life to shrink the particles down into the center over their lives. If you stagger the spawning of these particles it could produce an effect like waves moving towards the center.
Another option would be to spawn a larger number of smaller particles in a sphere and have them attract to the center point.
Edit: Now that I’m home and have seen the video, I’d probably try to do it with the first option. Start your distortion particles a bit bigger than whatever you’re distorting (ie. the central sphere in the video), and collapse them to the center with scale size over life. Tweak the curve and spawn rate to get the wave pattern you want.