This study has very low confidence. Many bird groups may have appeared completely in other regions than believed, and their current distribution can be relic.
First, the study suffers from "belief in selective dispersion". Why some groups of birds should stay and evolve 60 mln years around their supposed region of origin, when other similar groups successfully emigrated and immigrated?
Second, method of finding place of origin is too vulnerable to rearrangenent of lineages, and algorithms of treating speciose/divergent lineages (is 300 closely related tyrant flycatcher 300 proofs that suboscines appeared in South America or just one?)
Third, the study is fundamentally not statistically sound. Findings of supposed place of origin of a group of birds boil down to place of just two oldest lineages, and "evolution within one place" is conflating evolutionary events which took place millions of years away from each other.
Fourth, fossil record is too fragmentary, and finding unexpected fossils (like ancient hoatzins in Africa) is too common.