The short answer is ‘yes’ they all have to be the same.
Each TaxCycle installation that you want to synchronize with Dropbox should have its own (optionally private) Client Manager setup.
The Options/Folders are where TaxCycle opens and saves your tax files. So these folders will be set to where Dropbox looks for your tax files. On save, Dropbox will synchronize those changes to all of your workstations.
Client Manager will automatically index your tax files when they are synchronized down locally from Dropbox, so the Monitored folder(s) will need match those of Dropbox as well. If not, Client Manager won’t know where to find them and miss any changes.
Once you have setup your Options/Folders, on the Client Manager Monitored Folders options view, you can click the “Reset folders” button to have Client Manager use the same folders so you don’t need to enter them twice.