Hm, I'm not sure that article applies. That is the process for moving your data from one postgres instance to another, say because you are actually upgrading the postgres version.
But I'm not sure that process applies to changing plans, even under ordinary circumstances, if you are leaving pg version the same.
The wording when I upgraded to 'mini' gave me the impression that I didn't have to do anything else, my existing database would just change it's plan to 'mini' tomorrow, but be the same database.
But I don't exactly trust heroku to get it right anymore, alas. (Which is a bigger problem than the elimination of free plans -- the whole reason I was eager to use heroku, including for paid plans, is because I always did trust them to get it right.)
This is actually just a "hobby" project, that also can be restarted from an empty database if needed (it's http://rubyland.news), so... I guess we'll see what happens tomorrow? I believe my database will persist, just with a new plan.