I have it working in multisite, although so far I haven't gone through the whole process of configuring the site for SSL and setting up live tabs. But I've enabled Facebook Tab Manager in a multisite configuration and been able to create and preview tabs, with no sign of the error message you mentioned. Possibly what you're seeing is unrelated to multisite and is another issue, such as a conflict with another plugin.
Or maybe I just haven't replicated whatever issues are causing you trouble. You might want to copy and paste in the entire error message here or email it to me at email@example.com.
Does the error occur immediately when you try to activate the plugin? Or when you try to complete some action, after it has been activated?