It is illegal in AZ to have any tint below the rear view mirror....unless you have a note from your DR. (serious)
It is also illegal to have your windows tinted beyond 35% on the Driver/passenger doors.
I have NEVER met anybody that has been pulled over for this/or has even had a ticket concerning tint.
I just had my (new to me) car done in 15% all around with a limo visor on the windshield. It looks almost completely black from the outside unless the sun is hitting it from the side. ie: early morning or late evening.
To get back to your post....yes it is completely normal to have little bubbles in the tint for the first couple of days. Some of mine have taken over a week to go away! It drives me nuts, but I know it will eventually go away, or the guy will replace them for free.
FYI, Now that you have tint I would stay away from window cleaners that have ammonia in them. The ammonia can cut the life of your tint drastically. Buy a quality window cleaner, specifically one that states it is "safe for window tint".