Let me preface this by saying that I'm the PFDAVAdmin expert, but I'm not the DST expert. That said...
My current understanding is that the owner of the folder must run the tool against the folders they own. However, the tool will only update appointments for which that user is the organizer. That means if you have a folder where a bunch of different people can create appointments, each of those users would have to run the tool, and they won't all necessarily be owners... they could have other roles. So depending on your situation, just knowing the owner might not be enough.
The easiest way to approach this is probably to have the owner of each folder responsible for running the tool and manually updating any items that the tool won't affect. Or possibly have the owner identify any users that created appointments during the new DST range and have those users all run it against the folder.
So that's my understanding of the current approach to this. Hopefully someone will correct me if I'm way off here. :-)