I think you need to setup an LDAP filter, such that users listed must have the given group membership. From memory, this ONLY applies to direct group memberships, inherited memberships won't work (yet?)
To know you have the right ldap filter, get Apache Directory Studio, it will allow you to bind to your ldap server and perform queries based on filter. This will be far faster than guessing in your JIRA config. Prove the filter returns the users you expect, then use that filter in your LDAP user filter:
https://confluence.atlassian.com/display/JIRA/Connecting+to+an+LDAP+Directory
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