it sounds like you are experiencing what the Tint shop was talking about with 90's model hondas. I am not sure what year make you have and I am not going to guess from your sig.
But the tint is getting pinched in the upper front corner of both windows I am guess. the silicone is supposed to provide long lasting lubricant so that the seal will not put a ton of pressure on the tint and cause it to pinch at that spot. Down side to lubricant is that you will never really will have a clean glass, and if you do you will have a pinched tint.

Although the shop that you took it to allowed you to get illegal tint, possibly setting you and them up for legal problems down the road. no matter how well of job they could have done without that being addressed the tint would have pinched at sometime. I would have thought longer than a week unless your seal really sucks and you window won't even close completely, you know what i am talking about a quarter inch gap in that corner.