I have also sometimes encountered difficulties in getting seasons replaced when they have faded or stopped working the barriers.
I don't recall any such rule about the first day of validity from my days in the ticket office, but I do recall that it was a real pain in those days to replace a season, particularly if it was issued at a different station. The process used tog ernerate a fair bit of paperwork, but I would hope that there would be less of it now!
I suspect that the clerk did not want the bother, and hoped that the ticket would work later on today, and that if it didn't they would be on a rest day tomorrow anyway!