The original Kickstarter https://www.kickstarter.com/projects/1425492550/sesame-your-key-reinvented claims door open/close detection was built in.
Leave your keys behind: Just lock and unlock your door using the Sesame app on your phone. Better yet, open Sesame with a custom knock on your phone or door. Your keys, reinvented.
Log records: Receive a notification whenever your door opens or closes.
I'm actually not sure if this was actually delivered or not, certainly my lock only reports lock status not door status. Similarly with knock on door support - which implies an accelerometer in there.
If there really is a accelerometer then that could detect door closures. The timed locking is not really what was promised but its better than nothing.