The cloud edition of Manager has nothing to do with iCloud. You need to subscribe and pay a monthly fee. See https://www.manager.io/cloud/. No application is installed on your computer; you access Manager via a browser.
The desktop edition will create a data file that will only be accessible from the machine where it is installed unless you move the application data folder somewhere else. That somewhere else could be on iCloud. Then, if you install the desktop edition on another computer and also set its data path to the same location, you will be able to access the data from the other machine. See https://www.manager.io/guides/10348.
If you go this route, be sure the two machines always have the same version number of Manager installed.