All trains you take that are scheduled to depart between midnight and 23.59 count towards that day.

If a train departs from the station you board at before midnight but continues on it will not require a second day’s pass use. Once you leave that train and board another you will need to use another travel day.

This rule also applies to inbound/outbound travel, you have 2 full days to use in your home country, the numbers of changes allowed is unlimited.

Beware that boarding a night train before midnight outside your home country that travels into it will allocate your home country day to the departure date and you will have no more use on the arrival date. If this situation occours it is usually possible to split the allocation of the journey on the app to give the required allocation of the home country use to the next day without having to actually leave the train.

Alright, I don't understand the second response unfortunately. As an example: I'm traveling from Vienna to Berlin on the night train. However, I actually need to go to Hamburg, where I live. The day before, when I board the night train in the evening, is the last day in my passport. What do I do in that case?

Change your plans or buy additional tickets as that will not be within your validity.

Once you leave your overnight train the pass day use from the previous day expires, you cannot take an additional train without using another day.

Additionally on the last day of a pass validity you cannot travel beyond midnight on it. On a continuous pass this is the last day, on a flexi pass it is the last day of overall validity.

Alright, I understand. But if I understood you correctly earlier, can I also process my 2 days in and outbound directly in my home country? Without having to cross the border?

If your pass is say 10 days within 2 months dated for 10 Aug - 9 Oct and you are planning to use your 10th day to leave Vienna on the evening of the 8 Oct you can use your pass until the last stop that train makes in Germany. Your pass expires at that point and any additional trains you will have to purchase extra tickets for.

You will also require an inbound day to make this trip as part of it is in Germany.

In/out days are part of the overall validity and not in addition to it.

If however you wish to do that journey on the night of the 9 Oct you cannot as the pass expires at midnight on the 9th and would not be valid for the overnight train passing midnight.

To do that trip entirely with your pass you would need 2 travel days.

You would split the Vienna - Berlin into 2 parts on the pass, while remaining on the same train. As (assuming you are looking at NJ456) it enters Germany well after midnight you would just have to pick a station the train stops at after midnight, for example enter Vienna - Wroclaw for the 8th  and Wroclaw - Berlin for the 9th in your pass, this would then allow you the rest of the 9th to use your pass in Germany.