You need to add a normally closed relay which is triggered when the turbo timer starts.
It should open the ignition sense circuit of the alarm.
So... when you switch the car on, the alarm can sense the ignition.
When you switch the car off, the turbo timer kicks in and opens the ignition sense circuit.
The alarm thinks the car is off but the timer is still running.
You can now arm your alarm with the engine running on turbo timer...