The parties had agreed on a cipher suite using ECDHE, meaning the keypairs will be based on a selected Elliptic Curve, Diffie-Hellman will be used, and the keypairs will be Ephemeral rather than using the public/private key from the certificate.
I think it's important to mention that even with ephemeral cipher suites, the server's ephemeral public key is signed using the server's certificate private key and verified by the client, since otherwise one would be able to MITM the key exchange.
I think it's important to mention that even with ephemeral cipher suites, the server's ephemeral public key is signed using the server's certificate private key and verified by the client, since otherwise one would be able to MITM the key exchange.