I see two questions
"where do the elliptic curves in ECDHE-RSA are exactly used?"
I see this is as "How are elliptic curves used when it's RSA in ECDHE_RSA?". Well, check RFC 4492, Section 2, ECDHE_ECDSA - it's pretty good. Essentially, the server certificate is an RSA certificate (i.e. with long term RSA keys) but during the TLS handshake it instead send over a transient/temporary/Ephemeral (the E is DHE) EC public key to do DH. So the long term authenticity is confirmed via the server cert's RSA signature but the transient keys are derived via ephemeral EC keys (which then generate the symmetric key)
What upsides has ECDHE-RSA over DHE-RSA?
This is already addressed in the other answers.