Ann Gibbons explains the importance of the new possible stem anthropoid fossil teeth from Myanmar: "Out of Asia? New Primate Fossils Pose Origin Riddle".
The four molars were enough to show [paleontologist Christopher] Beard and team leader Jean-Jacques Jaeger of the University of Poitiers in France that Afrasia was closely related to another primitive anthropoid that lived at about the same time, but in Africa—Afrotarsius libycus from Libya. When the researchers examined the teeth from the two primates under a microscope, they were so similar in size, shape, and age that they could have belonged to the same species of primate, says Beard. Such close resemblance between an Asian and African fossil anthropoid has “never been demonstrated previously,” the authors write online today in the Proceedings of the National Academy of Sciences.
The paper  mentions an earlier candidate for earliest-known anthropoid, Algeripithecus from the Early Eocene of North Africa. They cite recent work claiming that Algeripithecus is an adapoid primate rather than an anthropoid.
Meanwhile, I wish that frame, "Out of Asia", would go away. People are already confused enough about the idea of "Out of Africa". Here we're talking about a time period literally 400 times older than the "Out of Africa" dispersal associated with the origin of modern humans. The evolution of early anthropoids was a process that unfolded over millions of years, not a sudden event.
Why do we care about the location? Knowing where early anthropoids lived helps us to better describe the conditions that enabled that process, including the forest and faunal community in which they evolved. So why not focus on that community itself, instead of the continent? If we have similar tarsier-like animals living in north Africa and southeast Asia, whether that's interesting or not depends on whether primates are unique or share that geographic distribution with many other orders.
- Late Middle Eocene primate from Myanmar and the initial anthropoid colonization of Africa. Proceedings of the National Academy of Sciences of the United States of America. 2012.