Domain User Belonging To Multiple Windows Group

If I have a domain user DOMAINuser1 who belongs to multiple window groups say DOMAINLookupConfigUsers and DOMAINAuditConfigUsers. In sqlserver, I would create two logins - DOMAINLookupConfigUsers and DOMAINAuditConfigUsers and matching users in the database. Then I grant LookupConfig role to the LookupConfigUsers user and AuditConfig role to the AuditConfigUsers user in the database. When DOMAINuser1 logs in, will it have both roles? I try to set this up but it does not seem to work. The domain user only picks up one of the role. Am I on the right track? If not, what is the proper way to grant multiple roles to a user when it belongs to multiple groups and each group has different privileges in the database.