To access your Animator files from more than one computer you only need to:
1- Log in with the same account credentials in both machines.
2- Make sure you publish all the changes you make to your projects in each machine.
When you first log-in on a new computer, you won't see the project's preview on the dashboard until you open each project, but all your work will be there!
It is necessary to publish in order to get changes between the devices. If the user doesn't publish, the project never leaves his/her local machine.
One other possibility, if this isn't working, is that you have divergent copies of projects between your devices, e.g. where you worked on the same project on two machines in two different timelines, without first publishing/syncing changes. In that scenario, "bringing in" latest changes won't work, because histories are incompatible. The best way to avoid this is to ensure that the latest version has been Published before editing on another machine. A good way to fix this scenario if you're already in it would be to Duplicate one of the projects, and then treat the two histories as two separate projects entirely. Generally, duplicating projects (akin to MyFile001.psd and MyFile002.psd) is a useful way to manage concrete different versions & histories in Animator.