Hi,
TARSYN is basically a gyro system that can't follow hard maneuvering. There is not much to say except that the heading gyro is slaved to a fluxgate to keep the heading in sync as you fly, though it can also operate in a free gyro mode of operation.
Basically if you fly the aircraft hard, in either roll rate or hard turns, then the ADI and heading gyros will quickly lose alignment.
There are all manner of precession programmed into the system as well.
If real gyros do it, the sim does it. :)
Best regards,
Tango.