We need to differentiate 'accuracy' and 'precision'. For precision: If you stop the RTC, you can write the prescale-register (TPR) by multiplying your 'milliseconds' by 32768/1000. With that simple extension your driver can easily read and write 'millisecond' precision.
As for accuracy, the default 32,768 divider CAN have the small adjustments mentioned (this would, however, negate the ability to convert TPR to ms with the simple 1000/32768 factor), and with that you could compensate the typical temperature-curve of watch-crystals, but ONLY if you are 'awake', at least periodically, to measure temperature and adjust the compensation appropriately. Another way to get 12ppm accuracy (~1sec/day) is to use an external part that already does this real-time temperature-compensation: SiTime: SIT1552AC-JE-DCC-32.768D. Takes a little more battery, but insures +/-10ppm 0-70C (extended temp versions available -40+85C, holds +/-13ppm).
