Vanguard

All LLumar Automotive products have >99% UV rejection up to 380nm. Glass itself screens virtually all of the UVB. Adding window film screens UVA and the remainder of UVB. UV rejection % drops somewhere around 21 points by the time you get to 399nm. A car's windscreen and SUV privacy glass reduces UV up to 95% and again, adding film boosts UV screening performance values.
 
What many don't know or pass on when buying for the purpose you  have stated, is that for those who do have serious UV sensitivity need replace the product every 3-5 years to maintain maximum protective performance from the applied film. Every 3 years in sunny climates and 5 years in moderately sunny climates.
 
As to verifying the product is the brand you requested, other's here have given good insight.
 
You can also look for a window tint dealership in your area that owns a EDTM SS2450 meter. This meter can verify the product and glass are in fact reducing the UV to 0-!%. Although, it will require a more sensitive meter to break down nanometer %'s; meters usually specifically designed for and available for sale to UV sufferers.

The fact that you didn’t get paperwork for it was done for cash isn’t necessarily suspicious . I’m a reputable Llumar dealer and I won’t give paperwork for a windshield tint as it’s legalities are questionable. I have only ever used AIR80 in a windshield because despite its questionable legalities, I’m all for helping customers with their skin issues with a tint that in no way is dangerous for visibility.
With that being said, there should be no reason why the shop can not show you the tint with lot number in a “bonified” box for your piece of mind . If they cannot , I would go right to head office and confirm that they at least buy that particular product. If they do, the odds are you are ok.
Also as a last resort , if you go to another Llumar tint shop who knows the film lines well, they can look at the job and should be able to tell you just by looking at it with a trained “Llumar eye” .

You might be able to contact Llumar and find out if they sell film to that particular shop ?  Don't know? 
 
I'm not a doctor by any means, but I'm pretty sure the issue with skin cancer is in the UV spectrum of exposure.  The good part is, all decent film will be 98-99% UV rejective.  This is a necessity for the construction of window film and plays a part in longevity of the film.  Bad part is trying to prove exactly what film you do have is going to be tough because you didn't see the roll.  Sorry.  
 
The CTX and Air 80 are better in the IR spectrum (what you feel on your skin) so you should feel conciderably cooler behind the film, but you can be pretty sure that you are protected from UV at this point. 
 
It would take one of the smarter people to confirm whether the CTX and other higher end films are better for the skin cancer thing than other films.  We know they are better for the feel of heat (iR) but I don't know that there is that much difference in the UV spectrum as far as more protection.  Maybe more UV-A or UV-B blockage one way or the other but that probably about it.  Again, just guessing on that part.