It has consistently been that way, even throughout the era of paper discs.
Previously, when I was selling, it was permissible to tax a vehicle during the last two days of the month, with payment commencing from the first of the following month. This practice is no longer allowed; even if one taxes a vehicle on the 31st, payment is required for the whole of the concluding month.
Previously, we could pay a little fee to extend the tax on new automobiles by one or two weeks, which was beneficial for meeting our monthly or quarterly targets. Otherwise, buyers may decline to accept the vehicle until the following month, resulting in the automobile being attributed to next month's sales numbers, which is suboptimal. It is unclear if new vehicle dealers are still permitted to do that; clearly, we could not do such action on the day of the plate change.