Splashtop Business supports a number of alerts and notifications, such as invitation accepted/declined, computer online/offline, and computer added/removed. Additionally, there are notifications you can manage that go to your customer emails. These notifications can only by configured by logging in as the Owner or Super Admin role.
Login to your account at my.splashtop.com, then click on Management->Settings. Then click on the "Set up notification emails" link. You can enable/disable notifications and configure who receives them.