Let’s start by clearing up one misconception. The TEM (aka BigFix) Server doesn’t KNOW anything about Active Directory. The BigFix server doesn’t query AD for anything. The BES Clients report information about Active Directory, and the Console displays it as a collapsible tree structure for you.
If your Computers are not connecting to Active Directory on a regular basis, even THEY may not know what Groups they are members of.
The BigFix Client will, by default, only check AD Computer Properties every 12 hours. You can adjust this setting, but setting it too low can have VERY heavy impacts on the BES Client performance (responding to Actions, evaluating properties, etc). I have a group that has been setting the Active Directory Refresh property to 4 hours, and I consider that a little on the low side. I would prefer 6-8 hours, but they insisted on 2 refreshes per Business day.
Unless you can resolve the issue with your Computers not reporting to AD because they are outside the network, there really is not going to be a way for BigFix to make use of any Group Memberships.
You might want to consider Semaphore files. The idea is that rather than relying on AD Groups that the computers themselves are never seeing, you can use BigFix itself to drop Text files in a folder (or add lines to a text file) kept under the BES Client folder (to protect it from nosy users).