Welcome,
We don't get the blue drive models in Australia, but almost certain it does have stop start feature. Unfortunately, Hyundai haven't been very good at getting this feature to work consistently. There are too many parameters which need to be met for it to work consistently. There are several posts on here about these parameters. One of the main ones is a strong battery charge. The good news is it makes minimal difference to fuel economy and isn't that pleasant to use.
I'm on the way out but hopefully someone else has time to find an applicable thread amd posta link here.