To add an AD group to sysadmin, you would do:
ALTER SERVER ROLE sysadmin ADD MEMBER "DOMAIN\SYSADMINS"
If this does not work out for you, it may be that you someone did not the users to the AD group.
You can inspect which security tokens that you have by running
SELECT type, usage, name FROM sys.login_token
If everything is OK, you should see the name of the AD group as well as "sysadmin" in the name column.