Martin,
There should be some misunderstanding on the feature.
The EAP Group Mapping will define which certificate will be presented by the RADIUS server based on the Username/NAS-IP/MAC.
The authentication as such will be performed with the info available in the AAA config. No need to play here with the EAP Groups:

You need the EAP Groups if the client is validating the RADIUS certificate.
The purpose is to present a specific RADIUS certificate.
I use the following use case:
I the check the Usernames like "host/computername.private-domain.local" for computer authentication and the via the EAP Group I check the username and I present a RADIUS certificate that was issued by a Root-CA available on the specific computer.
You can request the users to log-in with something like
[email protected] to ensure that you'll present an acceptable RADIUS certificate for the client.
If non of the EAP Group is matching, the default RADIUS certificate is presented
The default RADIUS is presenting a certificate from a public authority. It is usually a star certificate (for example *.public-domain.com).
I must use this because the BYOD devices do not have any Root CA from private PKI by default.
I upload this certificate in the "RADIUS Server Certificate"

Hope this help.
Mig