Just checked this feature. This is very good and different from other sites where the auto bet keeps on running if we move between the sites or tabs in the browser.
But sometimes people want the auto bet feature to keep on running while they check their emails or other stuff in other tabs. Maybe you can give both options whether to stop the auto bet or keep on running, depending upon the preference of individuals.
It's a good idea to let the users to select whether they want auto bet continues or not when they move to other tabs. And I think as long as the option you said does not exist, it's better if the auto bet continues. Because in this case users can easily pause the auto bet if they don't want it to continue. But those who want it to continue have to not move to other tabs.