This picture was taken directly below the roof in the 1st picture. You can see it is soaking wet. I do have a skylight on that roof but that has been replaced and sealed repeatedly. I always blamed the skylight but now I am wondering about the drip edge.
I'm sorry for your frustrations but what a sh!t job by this roofer. What even are those flaps hanging in the gutter; drip edge backup plan?
I'd like to see more angles of your roof line but I think this picture will illustrate how water is flowing on your roof.
If you're comfortable with ladders then grab a hose and pour water on your roof while you record the flow. You should quickly see whether things are working properly.
If my illustration is accurate then expect your fascia to rot in the next few years.
For the record, water dripping from your soffits is not normal. Keep investigating until you find the source and do everything in your power to make the roofer properly fix it. Presumably you paid at least $10,000 for this new roof so if they suggest patch-work such as silicone or some mastic then be aware that they are trying to avoid doing it right.