If the guest is in the space prior to the posted check out time, it should be as if they stayed the night before. So if they arrive at 6 am and check out is at 11, check in at 3, they cannot occupy the space before 3 unless you allow early check in. And if you allow them to check in before 11 then they are actually acting as if they were last night's guest. If your 130 am guest went into the space and used it, then they should pay as if they arrived any time after your check in time the day before, because you can't have another guest in the space that night.