there is no update mechanism or command implemented, You will have to wait for TTL is reached and groups updated. Alternative keep your "Authentication Cache entry TTL" low. Unfortunately you can expect performance degradation due to obvious reasons.
The MWG has Rule Engine Events to clear the cache. However, they affect all users (the global cache). They do not clear the cache entry associated for a single user/IP. (feature enhancement request needed)
For NTLM settings, there are two 'authentication caches': Authentication Cache and NTLM Cache.
The first setting, Authentication Cache (default 30 minutes), stores the groups for a client if they choose Basic authentication.
The second cache, NTLM Cache (default 10 seconds), applies to IntegratedNTLM auth. This cache stores groups (and other parts of the NTLM handshake) for the TTL -- eliminating the need for MWG to validate credentials with direct communication to the Domain Controller.
These caches are not stored on disk, so they are cleared when:
The MWG is restarted
The setting is disabled and configuration Saved
The events Authentication.ClearCache (for Authentication Cache) or Authentication.ClearNTLMCache (for NTLM Cache) are triggered in the Rule Engine.