Keep in mind that the liturgical day doesn’t end at Evening Prayer but at Compline, which is the prayer that officially and canonically concludes the liturgical day. It is the prayer that you say right before going to bed. Therefore, if you pray the Office of Readings at any time before Compline, then the readings should be of the current day. However, if you decide to pray the Office of Readings at anytime after Compline (i.e. anytime after you have gone to bed and have actually had some sleep, and regardless of what time you decide to get up), then it is presumed that the readings will be of the next liturgical day. (and of course, it would follow that you will begin the Office of Readings with the invitatory to open the new liturgical day).