I came up with a solution hope it fits you.
I left the offsets, the lengths, the tiles and the repetitions on their default value. Honestly I don't know if I can control the emission of particles when messing in those parameters. Hope someone here can say something about it.
I created two animations - one for the emition (b&w) to restrict it and another in the color channel so you could see how it could propagate.
What I recommend it's to create a small .mov file with an animated texture with the effect that you are looking for, instead of messing in the offsets or the lengths.
Hope it helped.