What triggers a “breakthrough reward”?

I think it something that shows up at random. There seems to be no “trigger” to activate it. It just shows up whenever every so often.

It can be random at times, it seems - but it also seems to get triggered when the game thinks you're stuck or having a hard time. Don't know if it's a break in your flow / pattern / speed of matching or what - but that seems to be an element in it as well.