We have a dusk to dawn light on the driveway and I have found the birds will head inside the coop and be on the roost almost always within 2 minutes of that light coming on. Rarely miss it by even 5 minutes. Sometimes sooner on dark, dreary days, but never later. It seems like they have the same light level sensor as the pole light does. And as for timing, the moment the last one goes in, the door shuts behind them.
Sometimes they all can be tricked into going in sooner, but that is hard to do. One or two will always hang back to thwart you.
And they come out when I get around to it. Usually it is early, but if I'm not around, that may not be until an hour or less before dark, if even that. If they have to stay in all day, so be it. House is setup so it is no real problem for them if they do.