prescribes such features for the song-like genres.

I am attaching snapshots from Sankirtanalakshanamu 15th Century AD work by Tallapaka Chinatirumalacharyulu

English translation and commentary by Dr Salva Krishnamurty. Biblio stuff in the cover page below. 

The book says Bharata, Dattila  and others say, yati, prasa rules for songs are in the lines of verse meters only.

But this is an instructional statement where to learn he rules. But is neither intended to be nor is a historical statement.