At the time this article was written, changing the database plan in the Tile configuration will not actually change the database plan for scheduler-mysql and scheduler-broker-mysql services in the org system or space scheduler.
If this is still the case, then this needs to be done manually.
Product Version: 2.10
The first thing we recommend to do is to take a back-up, then, you should be able to upgrade the scheduler db services with "cf update-service", as stated in the MySQL doc.
Something like this should work:
cf update-service scheduler-mysql -p "db-medium"
Another option is to delete and re-install the Tile with the new desired db plan and restore the db from the back up previously taken.