In chicken forums, there are two opinions on giving a broody chicks either from an incubator or from the feedstore: 1) do it during the day, so you can watch as needed 2) do it at night. I've given a broody chicks two times now. I think either way works, but with two caveats: 1) do it when it is cooler (either the morning or evening) 2) keep an eye on things.
In my experience, a broody doesn't notice much. I can add chicks and she just sits there. My broody is a nice girl, though. If your broody is mean, night might be best so she doesn't attack. I put the chicks under her wings.
Yesterday when I tried giving my broody chicks, I had a problem. The chicks didn't know she was there mom, and it was warm enough in the coop that they didn't need to stay under her. They ran around exploring instead of sitting under her like good little chicks. I had to keep tucking the chicks under. Eventually, everyone got the memo and this morning momma took them all off the nest to eat. So broody is broken and operation add-a-chick was successful.