Personally I think making this a rule is too much. It can be "strongly advised" that you arrive 15 minutes early but a rule? What happens if someone arrives 5 minutes before they start? They aren't actually late because they aren't yet being paid.
Yes I understand why it might sound unreasonable, and nobody actually gets in trouble if they arrive 5 minutes before they are due to start, but if they then proceed to make a cup of tea, a bit of toast or cereal, then have a chat about whatever, then they get reminded about the 15 minute rule. It's nice to have a laid back office with general chit chat not disapproved of, but when it's first thing in the morning usually when the phones are busiest, something has to give.
So it is always explained the reasoning behind the "rule", I mean it makes the working day have a more relaxed feel with nobody being asked to be quiet and get on with some work.