The light has a dual function. It blinks when the car is off, informing you, and warning others, that it is protected by an immobilizer. The immobilizer is immediate. It is intrinsic to the power-up function of the car, in conjunction with the power ECU and HV ECU.
When you press Power, the ID of the fob is checked, and if valid, the power module puts the power mode to the intended mode, up to Ig-On. If you are intending to go to READY, then the HV will request from the immoblizer if it is really OK start. This request goes over a dedicated communications that is a paired shared secret, configured when the two ECUs are broought together at the factory, or when one is replaced.
If you have the alarm system activated, then the immoblizer symbol will stop flashing when you lock the car, indicating it is on delay to arm the alarm. After 30 seconds, it starts flashing again, indicating it is armed.