that sounds like you are being fobbed off to me, but make sure you get the same amount of fuel back in it when you collect it
the fact it only happens at very low temperature could indicate something shrinking due to temperature allowing a small airgap to allow fuel to drain back
they said 2 misfire events, but you have had more failures to start than 2?, the misfires could be the engine sensing insufficient fuel to fire correctly as air is purged from the fuel system / injectors when you sense it trying not to stall
silly question if you turn the car onto "accessory" by pushing the start button once without your foot on the brake for a few second before putting your foot on the brake and pushing the start again to start the car as many cars run the fuel pump when the ignition is tuned on to prepare the car prior to the driver actually starting it
may also be worth contacting the importer again just to explain politely how you feel and that you may feel the dealer may not have adequately investigated the issue from the response you got, and that you will see if the issue has been resolved (as they may have tightened a few things up but not said when they drained and refilled the car with petrol)
As a last resort the other option we have in the UK (I think it comes from EU law) is the sale of goods act, we have the option to reject a car in the first year if there is a fault which can not be resolved that affects the cars reliability or makes it not of suitable quality, BUT the dealer has to be given reasonable chance to fix the fault (in the UK I think they have 3 chances to fix it), if it happens again it may be worth checking with a local consumer protection organisation and looking at your contract to see if you have something similar, but hopefully I won't come to that but it is useful to bargain from an informed position I needed
I am SURE I am being fobbed off, but I can't reproduce the error in front of them, and they know it. So, from now on I have a Fiat: today starts, tomorrow doesn't. No trust in the car at all, if they didn't fix anything. The car is not new anymore, have to live with from now on.
And this will be shared with the importer, I am sure, because they show interest themselves. By the way, I was very polite to them and only expressed my feelings, didn't ask for anything. Probably they are really into that mysterious thing called "customer satisfaction" which is rare here.
I thought of the ACC mode by the way
On some older cars, I let the pump work for longer time, true. But here I don't think its legit - the car should know and understand how to start the engine. And it tries 3 times - not 1! - after the button push before it gives up. To me, that's pretty enough to build fuel pressure.
As for the misfires, they clarified that:
1) they meant not 2 events, but 2 cylinders (misfires in 3rd and 4th) - said the car was storing only one cylinder per error, but not how many times it misfired. This is plain bullshit, I know it well from VAGCOM and generic OBD. Yes, misfires do produce different error codes for all 4 cylinders, but the increment is stored as well. This means, 2 cylinders misfired several times each.
2) it is obvious to me that "a misfire" is not much more informative than "vertigo" in medicine: the cause could be anything from lean/rich mixture to fuel pressure to ignition coils to injectors etc. What I know, no ECU program will give up starting engine after a misfire.
I wonder if Hyundai has this problem on non-hybrids (on push-button start gasoline engines) - googled it, but found only obvious brake switch problems, which is not my case.