When Castle and Beckett arrive in the Hamptons, the sun is just starting to set. It takes about two hours to go from Manhattan to the Hamptons, so it would have been at least 7:00 pm before they got there. The sun sets in October there a little after 6:00 pm.
When Castle and Beckett are sitting in the holding cell Deputy Jones tells them that Chief Brady wants to talk to them. Beckett jumps up from the bench but is held back by handcuffs. She is not really cuffed to the bench but merely holding them in her hand.