NO, this is not so. A travelday covers all DEPartures on a calenderday=untill 23.59 the latest, you can in any case still finish the trip, on the train you were on till after midnight, or even on a nighttrain till destination. But from 0.00 the new day starts.
Its quite logical: otherwise could do a 4 day trip from PorTugal to FInland on 1 travelday, as its a lot of connections.
If you can tell us for what day or what connection you ask this, perhaps we can give alternative suggestions to save you that travelday. Or by yourself: find train on bahn.de, click on train nr, then you see all stops from start till end. Find a stop <23.59 and check how you can reach that station-then you could do it! You can travel as you like on a travelday-even going same line backward! Note that about any nighttrain needs also a REServation
(note-untill some years ago there was a different rule-that is why some people get confused).