Did you fix this or is it still a problem?
So to summarise, you're seeing the RTC run fast when there's other CPU activity and it is running from the 32768Hz crystal.
My first guess would be that you're getting noise on the crystal inputs, either directly, from nearby tracks or on the oscillator power supply.
The CPU is running fast and so are all the noise sources. The crystal is running very slowly compared to this. 32768Hz has a 30us period.
What I'm thinking is that instead of the waveform from the crystal into the MCU being:
--------------------------___________________-------------------------_________________
When there's noise present you're getting:
--------------------------_-_______________-_--_----------------------_________________
And the occasional noise pulses are counting as extra clocks.
Add some more filtering to he power supplies. Try putting some more capacitance from the crystal oscillator pins to ground.
Put a CRO probe on them - that alone might fix the problem.
Check that the crystal is being driven hard enough. Or too hard perhaps.
Check the PCB layout to make sure there are no signal tracks under the crystal or near the tracks from it to the CPU.
Good luck,