Somethings missing in your description, and I’m not quite sure what it is.
First of all, if they nailed the first layer of membrane it is possible they installed a modified base sheet and not a smooth-surfaced APP modified bitumen roofing membrane. If that is the case, then it doesn’t make sense as to why they torched the side laps. If it is a smooth-surfaced roofing membrane, then the roofing contractor should not have nailed the first layer; it should have been torched down or adhered. Of course, the contractor may have just used a smooth-surfaced membrane for a base and torched the seams to provide a pseudo 2-ply modified bitumen roof system. If you can tell me who the roofing material manufacturer is I could probably help you better.
Now, lets talk about your problem. Do you have blistering or wrinkling? If you have blistering that is not a good thing and likely won’t go away depending on where the blisters and located and what caused the blisters. If the membrane was installed using a cold-process adhesive, then the blisters WILL go away in time. However, if the system was torched down as you say I suspect the blisters are between the two roof membranes and likely won’t be going anywhere. If you have wrinkling instead of blistering, this could be an application problem, or is could be caused by material shrinkage. Once again, I’d be curious whose product you have so I can know if it contains a fiberglass or polyester scrim, or both.
As for what you have. It is most likely an APP modified bitumen roof system; however, there are some torch-grade SBS systems. Still, my bet would be on APP (Actactic PolyPropylene) as the asphalt modifier.
Anyway, I’ve got to go watch the Steelers play the Browns. I hope I’ve at least started to answer your questions. In the meantime, take a look at what the contractor proposed, any wrappers or materials they may have left behind, or anything else that will tell you whose material it is and maybe I can help you more after your next post.
One last thing. You say the roof drains to an internal drain. Is there only one drain, and are there any emergency overflow scuppers? If there are scuppers, how high above the drainline are they located???
Anyway, get back to me and I’ll try and answer any other questions you may have.