I would of nope'd out of there as well. From my experience, tint should be done on the inside of the car, so I don't know why they are touching the spoiler or burning any paint.
The place I went to was extremely clean, even with it being the middle of winter and snow slush was everywhere outside. I didn't pay until the car was finished, and when I picked it up he admitted two windows weren't perfect (The top edges of the tint had a slight nick from cutting the film wrong. I probably wouldn't of even noticed it if he didn't point it out) and wanted to reschedule right away. Even gave me a discount on what I was going to pay.
I would definitely look at the reviews of places around you, and not just go to the first place you see. Sometimes it's worth paying a bit more, or waiting for an appointment to get what you really want. After all, you will be the one looking at/through it every day.