If you are publishing a contract and the email notification is not being sent to the client you should ensure you have the "Send Notification to Client?" checkbox checked in the Default Optionsof the contract. Even if you fill out the email address it will not send it alone, You have to tell the plugin to send the contract and this has to be done per contract. We do this because you may want to test it before sending it to the client, so this gives you an opportunity to verify it before sending the contract to your client.
If this does not resolve the issue, ensure that you have the Administration Email Notification set in the plugin settings.