(Notice for future readers: The following is based on an interpretation of FirstGroup's terms and condition. For what happens in reality, please see @gerrit's answer.)
In their trading terms, FirstGroup mentioned the following when they clarify validity of mobile tickets:
4.2. To avoid confusion, the validity of mobile tickets is the same as for traditional paper variants. i.e. the first day of validity refers to the remainder of the day of activation and a period of grace is given beyond midnight to allow local services to complete, and not a 24 hour period from the point of activation. [...]
Hence, a "day" for FirstGroup ticketing purposes ends at midnight (unlike TfL which is 04:30), and a day ticket's validity immediately after midnight rely on a grace period provided by FirstGroup.
If I understand the definition of "grace period" correctly, it means one should be able to take the 00:05 bus back to Reading with their day ticket acquired the day before.
This period of grace is implemented on their electronic ticketing system, mTicket. In their FAQ, they've mentioned:
If you're using a day return ticket it will expire at around 2am.