The phrase "the Beyond timeline" is problematic. The animated series and most of the prior BB series (including BB Unlimited and BB Universe) all seemed to be part of the same timeline, and presumably took place on Earth-12, if the Multiversity Guidebook is to be believed.
But the Terry McGinnis who appeared in Futures End was not from that time line, but allegedly the future of the mainstream DCU. And then he came back to a point in time 5 years in the future of the main DCU. And then he died in Futures End and 5-year-future Tim Drake took over the suit, and then went back further back in time to prevent that 5-year-future from happening and then he got flung forward in time to another timeline where Brother Eye had created a dystopia because that is what computers think best (or something like that). So an alternate future that might, possibly, be the future of the current DCU but, really, no way to tell. So Tim cleverly defeats Brother Eye, the brilliant computer (that, to preserve its safety, disabled every teleport except for the one that was standing right next to it). And then Tim, stuck in this future, takes over the role of Batman and fights a few villains, discovers that Brother Eye was even more incompetent than at first believed and failed to kill off the future Justice League as we first thought. So they were brought back. And then Tim finally tumbled that, in this future, Terry never did go back in time and was, in fact, still alive. He finds Terry and Tim then hands back the suit and drives off into the sunset (where he promptly disappears) and Terry resumes being Batman.
So that is where we are where Rebirth kicks in. It is a Terry in a future that is NOT the future of the animated series or any of the other prior BB books, but is the continuation of the timeline of the post-Futures End BB. You will note that the hideous dystopia that Brother Eye created seems to have been fixed, since we now have rich and poor again (as opposed to everybody miserable as the brilliant computer thought best). And the massive starvation that everybody was facing in the early Tim-Drake-BB series seems to have been miraculous fixed. Perhaps because of the Not-Dead Justice League that we have not seen since they were found to be Not-Dead.
Consider yourself filled in.