I was wrong in my assumtions yesterday due to my loose memory - today's test has shown that the top-up made on station doesn't become visible online immediately - the balance you see at the site is always the one of yesterday. So the once-a-day-transaction theory is consistent.
The online system is even more detached - e.g. it only shows travel history for the journeys paid for online for some reason.
Okay, now I understand that.