It's normal, will run for 10 min after ignition off.
Only runs when temp is above specified level. This was an add on to the FD RX-7 to combat high engine bay temps.
One of the triggers on the FD RX-7 was that the main (non-A/C) fan had to be running ~1 minute before the car was turned off.
I'm sure the triggers are very similar on the RX-8.
The FD RX-7 had a separate module behind the ECU that had a flying lead comming out of it that could be attached via a switch to ground to turn the fans on any time you like.
By doing this ~1 min before turning off the car you can force the fans to stay on after the key is out, about the only use I've ever found for a turbo timer.
The only caveat was that the switch had to be turned off once the fans kicked in after the car was turned off, or the batery would drain from the open circuit.