Both KMS and CloudHSM are FIPS 140-2 Level 3 and AWS claims they cannot read private keys from KMS. The main difference is KMS uses IAM and the AWS REST API while CloudHMS uses PKCS #11/JCE and a separate permissions system.
Actually, they wouldn't really know unless this domain is used. I guess they check the `Host` header to get the domain that targeted this IP and then check where the MX are hosted.