What date should I put on a paper that I hand in to my teacher?
Regardless of whether it is homework or any other sort of technical document, the correct date to put on a technical document is the date of its most recent revision.  If the history is important, other dates can be added as well (e.g. the submitted/revised/accepted dates on some journal papers). 

As for your professors never saying anything... they likely had no reason or even ability to discriminate between the different systems you used to date, and it likely did not matter for the purposes of the class.