Some do. Regardless of where you are traveling, you are expected to abide by the laws of that state. Some states explicitly have exemptions for out of state vehicles regarding tint laws, other states (like TN) require an officer to prove the tint violates the state of vehicle registration. In a few states, some cops will stop you for dark tints (as probable cause for the stop) and as long as you roll your windows down before the shows up at your side and don't give him any lip for the stop, you won't be cited. Some may cite you knowing you won't go to court and fight it (unless there are additional charges, it's almost always dismissed by a judge in every state).
It's very rare to be pulled over for window tint and then be cited
only for window tint. Far more common is to use the window tint as probable cause for the stop, and then find additional charges (suspended or expired license or insurance, drugs, etc.) and then the window tint is just one of the many charges filed. If you're pulled over for dark tint, and you don't do anything else illegal or give the office any lip, you'll be sent on your way with at most a warning.
Probably half the states' tint laws apply to vehicles operated on that state's roads, but rarely enforce it as a sole violation for out-of-state vehicles, probably 15% of the states allow really, really dark tint, anyway, and the rest have the laws written to apply to vehicles "registered in this state."
I've had mine tinted to a pretty dark 35% for 10 years, and have only been stopped once for tint in a state that allows only a really light tint (Iowa, 70%) and could have gotten an equipment citation, but didn't because I didn't give him any lip and was light and cordial with the officer. I've spent a lot of time in states that do not allow any tint at all and have never had a stop or anything said to me about it. I don't worry about it or even think about it. If I were stopped once a month or something, I'd just remove the tint and be done with it.
EDIT: Forum where you read it from the cops themselves
Window Tint Enforcement Action | Officer.com