The remote start mazda installs (at least on my MZ5) is an open loop. It does not know if the engine has 'failed' to start. So it will not 'retry'. So it will go on to complete the routine, the setup assumes everything is 'all and well' except the engine did not start. If you wait longer it will end the sequence after few minutes. And you can try again.
For really cold day, and I'm at a distance, I start the car.. I see the light turn on.. if the light turns 'brighter and stays brighter longer' it tells me the engined had started. If I'm not sure, I just 'stop' the engine using the remote.. then I try again. 2nd try usually assures start up. 3rd will work for sure.
The remote starter I installed in my old buick is far superior than the one that comes with mz5.