I have recently checked with the Tapatalk staff, and it looks like Tapatalk is not written well to accept custom pages or new tabs. As most of it is pre-compiled as a mobile app and it lacks a sufficient API to make a lot of necessary integrations, the only real way to make a Tapatalk integration would be for us to fork the Tapatalk code, compile and support a separate mobile app, and force all your users to download it in place of their Tapatalk apps.
Because of this, I must decline this request, until such time as the Tapatalk devs implement a more useful API.