None of the US spec Tucson's have an immobilizer key. You just have a regular key.
Also, Hyundai does make a remote start for the Tucson. You might want to look into that. We've had to remove several remote start systems at our dealership for the new Hyundai's because the aftermarket ones hack into too much of the harness. The Hyundai system is almost completely plug and play. They are a little on the pricey side though. List just for the kit is $351. I'll sell you one for $300 if you want to try to install it yourself.