As the climate warmed, sea levels rose, flooding low-lying coastal regions and turning major valleys into bays. For much of the epoch, for instance, Florida was almost entirely underwater. Further north, however, it was still connected to Asia (and Greenland, although that's less significant in the grand scheme of things). Perhaps because the land bridge was both far to the north and relatively mountainous, not many animals seem to have crossed it, but that changed in the Early Miocene as the climate began to improve, and only increased as the epoch wore on. And, for whatever reason, most of them were heading east - into America.