How does one NOT save Messages history upon new login in El Capitan on iMac?
The pref doesn't say "Save history when you quit or logout" it says "Save history when conversations are closed" - i.e., when you hit the X to get rid of them - either permanently, or temporarily, depending on that pref.

If you want to delete the archive itself, you'd have to do that manually.
Files live in ~/Library/Containers/com.apple.iChat/Data/Library/Messages