I think he probably used scientific dating techniques. Not having read the study, I have no idea which techniques he used, but if you're interested, your local university library probably subscribes to Paleontology and I'm sure the study goes over its methodology quite sufficiently.
Abstract:The age and depositional history of Dominican amber-bearing deposits have not been well constrained. Resinites of different ages exist in Hispaniola, but all of the main amberiferous deposits in the Dominican Republic (including those famous for yielding biological inclusions) were formed in a single sedimentary basin during the late Early Miocene through early Middle Miocene (15 to 20 million years ago), according to available biostratigraphic and paleogeographic data. There is little evidence for extensive reworking or redeposition, in either time or space. The brevity of the depositional interval (less than 5 million years) provides a temporal benchmark that can be used to calibrate rates of molecular evolution in amber taxa.