Controlling which visitors the chatbot is allowed to talk to is done in a similar fashion how access rights are given to human customer service agents. The website can be divided in smaller pieces and chatbot can be configured as the main chatter at some parts of the website only. For example, one could decide that the chatbot takes all the conversations that are started on the front page, but any conversation that is started at the 'Contact us' -page is directly routed to a customer service team.
The same configuration can be applied to automated messages. When a visitor replies to a proactive chat message, the chatbot can take over the conversation on certain pages, but not on the others.