A mink attacked a friend's flock in the morning not too far from your area. I think that generally nocturnal animals will hunt at night, but they can still do it in the day.
We had a hawk do an evening surveillance just tonight before dusk.
I think you have to decide what works for you and what you feel comfortable with. I have 4 chickens so feel like I don't have enough to lose even one. I just recently aquired ducks. So, now a new worry added.
My chickens are in a small run and coop during the day and if I am out there, they are allowed out in the open run. I was cleaning a playhouse that I am planning to use as a duck house just the other day. I thought it would be good to let the chickens out since I could keep an eye on them. They were out for less than 30 min and a hawk was circling (not sure if it is the same one as this evening's hawk). I rushed them into their safe area. How brazen of the hawk to do that with me in sight.

The ducklings are still tucked away indoors, so they are cozy and safe. But, soon, I have to decide what to do with their area.
What size of run do you have?