So if you check-in at 3.59 pm in the north of the Netherlands, and go to the south to arrive around 7.00 pm in the south of the Netherlands and you only use trains from 1 company (like NS) the whole journey will be considered off-peak hours. Even if by the time you arive in the south the peak-hours will already be over.
Most trains run with NS but some regional lines have Arriva (Deutsche Bahn) or Keolis (SCNF).
Additionally there is a 5 minute grace period in your favor, so if you check-in at 4.04 pm it will stil be off-peak.
And because the whole thing is rather confusing for those not already familiar with the system there you get to do it wrong once a year and get your fine waived if you call the train company.
And yes there's little queues just before 06.25 pm every day of people waiting in front of the check-in gates for their pass to become valid (especially on fridays when the weekend-pass will become valid).
Transfer don't change it, they're all part of the same trip. Going out of a station and then back in also doesn't interrupt your trip. As far as I know you need 60 minutes of being "out" of the train system for it to be considered a new trip.