How do you know it was not an "active" strategy? You seem to think that the only way such a thing could happen is if the lizards convened and made a group decision to use higher perches. Lizards could individually decide to spend more time on higher perches because that is where they are finding more food. Foraging animals, from insects to mammals, make decisions like that all of the time. The net effect would be that, on average, the population of lizards ends up spending more time on high perches. Thus, the change could be an "active" strategy with no group decision making required. The very short time frame for the initial behavioral shift -- "a few months" -- suggests that it most likely was a deliberate change in foraging behavior by the anoles.
...most do exactly what their parents did.
Again, how do you know that? You are assuming there is virtually no plasticity in an individual lizard's foraging behavior; i.e., that it is completely determined by genetics. I don't study anoles (and I'm guessing you don't, either), but I think that is unlikely. There is a great deal of research showing that many kinds of animals, from arthropods to vertebrates, match their foraging behavior to the distribution of resources in the environment.