Yes, it does.
Like usual with most of my obscure questions, I managed to finish my hunt and answer it on my own. I managed to get an outbreak to one away from dispersing. Auto battling, Minior using Explosion, and running away from a Minior Core all cleared the outbreak, while immediately running away from a Meteor Form Minior did not clear the outbreak.
Interestingly, even though I activated a Minior's Shields Down and got it back above half health to return it from Core Form to Meteor Form, it still despawned and dispersed the outbreak when I ran away.
I also got a bonus shiny Orange Core Minior while testing so that's neat.
Thanks for helping, me!