After messing around with the remote start a little bit more and talking with someone at FCA I have determined -- that in my case at least -- the remote start was user error on my part.
My vehicle had the body control module update completed at the time of PDI, so my vehicle hasn't exhibited some of the issues that you may have experienced.
Anyhow, as an FCA loyal customer I tried to use the Giulia's remote start system in the exact same fashion as my Chrysler, Dodge and Jeep vehicles in past. After all, the passive entry fob and remote start button looks the exact same, right? Well, not the case.
I usually instinctively press the 'lock' button on the remote before pressing the remote start button twice to remote start the car. This works fine on my pre-Fiat era FCA vehicles, but not here. As it was explained to me by FCA, pressing the 'lock' button on the Giulia's system temporarily 'wakes' the alarm system and keeps the vehicle from accepting the remote start command (lights will flash and vehicle will honk, but not remote start).
Simply put, press the remote start button twice and nothing else, otherwise remote start won't work (even if the horn may honk and the lights may flash). Also, after locking the vehicle and walking away from it I have noticed a need for 10 minutes or so to pass in order to remote start the vehicle once more (not that this would come up often, but just trying to try all sorts of cases). As FCA explained, this time is needed for the security system to be in a state to accept the remote start request.
Any questions, let me know... maybe I can get some more detailed answers from FCA.