I would imagine that auto start/stop is engaged automatically when switching to Eco mode because this is a significant part of what makes the car "economical" - presumably, you're driving in Eco mode to save gas.
Starting the car in Comfort vs. Eco may have something to do with ensuring the car "warms up" or has full-on utilization of system as usual? Not sure. Obviously auto start/stop doesn't engage until the engine is warm, battery is at solid charge, etc.
I don't ever use Eco mode, though, so I'm not the best one to comment on it!
