No, this is not right. Envato does not manage licenses for you. It only accepts payments from buyers and stores licenses keys in its own system. If author wants to manage licenses and ensure the same code is not used to perform multiple installations, he needs to create such a management/verification system on his own.
Envato only provides API for author, where he can verify if code exists. Everything else (checking if code is in use, etc) needs to be done by you from scratch. Or you can use an existing licensing software for this.