Hi @celestialpainter , I’m Chen, the Wix Chat and Inbox product manager. In case a visitor sends a message to the business, the business will first get notification in Inbox and in the mobile app. An email will be sent in the case the business owner didn’t open one of those notification and didn’t read the message after more than 5 minutes that it arrived.
So if you won’t open the notification on the web and mobile after more than 5 minutes, it will get to your email address.
Inbox/Chat messages will arrive to the email address of the user that he set in his account settings.
Let me know if you have any additional questions 