By default each container is considered a separate server so TKLBAM works within each one as an individual server. But AFAIK if you run TKLBAM on the LXC host it won't include all the containers inside (just the config); although TBH I've never checked. Why not test it out and see?!

I have no doubt that it could be configured to what you are asking but unless you are happy for a really big backup (i.e. include each of the containers' whole OS); or to spend a ton of time developing a configuration to do that more efficiently, you're probably better off just backing up the host and the individual containers independently.