When reading older papers how should I interpret the use of "Late Tertiary" and "Early Tertiary"? Would these periods equate to Paleogene and Neogene, or was there a different accepted boundary age between the Late and Early Tertiary?
I think this is very hard to answer this question as it is exactly this ambiguity that caused the International Commission on Stratigraphy to discard the names Tertiary and Quaternary for there are no clear limits to these era's. For example, the name Quaternary was only introduced some 70 years after the name Tertiary (source), and Neogene covered both the last part of the Tertiary as well as the Quaternary era (source), until in 2009 the Quaternary was reinstated as a period while at the same time redefining the boundary of the Pleistocene (source), so interpretation should take into account when the article was written as well.
The meaning of Late and Early Tertiary is therefore dependent on the context, and is probably only safe to be interpreted as relative ages (unless exact ages are given, but in that case there is no question of interpretation), not well defined periods in time. It might help to look for articles by the same author or from the same year to see what the common interpretation was at that time.