To me this usage of "on" feels incorrect. It would have been fine if the author had left out the preposition entirely,
Unconscious since late the previous Saturday evening, Sir Isaac Newton.
In any case the context makes more sense now. This is an example of what I think is called a participle phrase, or perhaps just an adjectival phrase. Since the phrase doesn't contain a verb, the tense is implied by context,
Isaac Newton, (the person who has been) unconscious since late the previous evening.
It's possible the author is mixing this with a related expression, "on the evening of ..." This is used to give a time frame to isolated events, but not to events that continue from a particular moment in time.
Isaac Newton died late on the evening of March 20th ...