You are mixing up key exchange and authentication. Key exchange is done so that both parties agree on the same encryption keys. Authentication of the server is done to make sure that the client is talking to the correct server and not to some man in the middle. The RSA/ECC key in the certificate is used for authentication. In case of RSA key exchange the RSA key in the certificate is also used of the key exchange but with DHE and ECDHE key exchanges the certificate key is not used. This means you can combine ECDHE key exchange with both RSA and ECC certificates.
For the deeper details see How does SSL/TLS work?How does SSL/TLS work?