It seems likely that Tavia's group and Carver's group are the same group. Very possible that Carver was the voice on the other end of Tavia's radio (yeah, I know it was a different voice actor).
Carver seems to be running some kind of cult compound. He went to pretty extraordinary lengths to get "his people" back. More understandable considering that Rebecca is carrying his child but even so – a 5 or more day trek is going pretty far to bring back some deserters. Also, if they've got enough to open up full auto on a group of walkers ammo is obviously not in short supply.
I wonder if the Spanish-speaking guy caught by Roman in 400 Days was with Carver's group. It's a pretty similar tactic to the one used when he sent Bonnie to scout out the ski lodge. It also ties in with the conflict that seems to have gone on between Carver and Roman's groups. Roman was dead at the river alongside the people that attacked Clem and Christa. Does that mean Carver now has Christa? I think that's highly likely.
If that's the case how is Christa going to react when she sees Clem arrive in the compound with another pregnant woman? Clem and Rebecca have bonded to some extent now (at least made a truce). Christa evidently lost her baby at some point while she was with Clem. Seeing Rebecca is going to stir all that up. I expect we'll get some back-story on what happened to Christa's baby.
So Carver and Roman's groups fought over Gil's diner resulting in Roman abandoning it. Carver then sent Tavia to scout the place out, see if anyone was still there and bring them into the fold. For all that Tavia comes across as a decent person I guess she believes to some extent in what Carver is doing. At least believes that it's better than the alternatives. Maybe she thinks that if they're at least safe from walkers then working from the inside she can push the community in a better direction.
Bonnie is with Carver. I don't think she likes his methods but she's a recovering addict & looking for something to belong to or believe in and Carver provides that. He provides moral certainty and direction. It's very possible she may ultimately side with Clem, though.