Simple problem. The alarm has a wire that is used to sense when the key is in (KEY SENSE wire). Typically yellow, but wire colors vary with different alarms so yours might not be the same. Check the installation manual for your alarm.. most manufacturers have them on their websites.
Anyway, if your turbo timer is installed correctly, you'll notice that the Accessory circuit (radio, cig lighter) goes dead when you take the key out and the timer starts counting down. That's because the turbo timer is supposed to keep the Ignition1 (motor/ECU) and Ignition2 (radiator fans, heat/vent/AC) powered while it is counting down. Verify that the Accessory circuit goes dead during timer countdown before proceeding.
What you need to do is take the alarm's key sense wire and move it from Ignition1 onto Accessory. What that does is, when you turn the key OFF and the timer starts, Accessory goes dead and the alarm thinks you've shut the car off. Doors will unlock (if you have auto lock-unlock on your alarm), and you'll be able to arm the alarm while the timer counts down.
The only drawback to this solution is that the alarm can arm while the timer is counting down. That means if your sensors are set too sensitive, the running engine will set the alarm off. There are ways to interrupt the sensors while the timer is counting down, but that's a different project.
Just so you're armed with some info, here's your key switch diagrams..
WHITE (Constant +12v)
WHITE (Constant +12V)
Always check to make sure the wire colors on the chart are correct before using it.. verify with voltmeter before installing. Standard stuff, do at your own risk, blah blah blah.
Let me know if that fixes it...