The Mishna Brura (320:59) says that coloring on Shabbos is only assur if the color will remain permanently, but if you color something that will disappear after a short period of time you are Patur. The Shaar HaTzion says that although you are patur it is still assur. What about wearing Photogrey glasses which turns into sunglasses when exposed to the sun and lose their color when out of the sun? The Piskei Tshuvos says that Igros Moshe, Btzel HaChochma, Shevet HaLevi, Mishneh Halachos and others all say that it is permissible.
The reason is that this is not considered coloring. When the sun reflects off the lens, it appears colored but nothing actually changed in the glass. This is similar to a mirror where by standing in front of the mirror you can change the image on the mirror but it is permissible since you haven’t done anything to the mirror itself. Revach
Rav Moshe has a teshuva that permits it since it is not coloring but rather revealing the color (to the best of my memory). He calls it “photogor”, I believe
Sorry, but you can’t compare this to a mirror. In a mirror, you move away and the reflection is away; on these glasses, the sun changes the color of the tint and actually changes the color not just the appearance and it takes some time to fade away after leaving the sunlight. The reasoning is due to the indirect manner and temporary nature which does not amount to Tzoveia.