The AeroFS Desktop Client does not support having two instances running on the same computer at the same time.
If you would like to completely switch from one user account to another, you must first unlink your existing AeroFS installation using the Preferences menu and then reinstall using your second account. Your data will remain on your device after you unlink.
It is possible to have AeroFS Team Server and AeroFS client run together on the same device. Just make sure that you have enough disk space to store all the data if you choose to store Team Server data locally.