Tint simply makes glass darker. If your window film does not block UV, etc. then all you have is "darker".
There is some kind of coating on the clear glass roof that is blocking all kinds of heat rays from the sun. Sorry to those who are scientific geniuses and don't use the term "heat rays".
'Darker' means (pretty much) less 'heat rays'. Visible light represents most of the energy in sunlight, though InfraRed is quite large as well. UV not so much, and plain glass already blocks most of that (and much of the IR) anyways.
[see my post at the top of the page]
Thank you kindly.