The doors will close a predetermined number of seconds after they were opened - since the doors do not open automatically as per the tube, they will all have been opened at different times and thus, close at different times.
If they are not being locked, they will reopen if they detect an obstruction, if they are, they will of course attempt to close regardless. This seems to be the same as most EMUs to be honest, Electrostars included.
The only difference in functionality I've seen is that if someone presses the open button but does not actually pass through the door, it'll close again almost immediately rather than waiting the usual 30-45 seconds.
What I assume you're referring to here is that, the 'climate control door close' (i.e. closing on a timer rather than because the driver has initiated all doors be closed) does not cancel if someone walks out the door just before it happens, it will only cancel if they're passing through the doorway as the doors are actually closing.