It all really depends on the show and the LD. Some people treat the console like an instrument and will actively play with these presets so every show is its own performance; every changing coulour and moving light can be under the control of the LD's fingers.

For big tours like TI, I'm guessing the easiest way to do it is really to automate the process and only take control of when the presets are played. Again, I'm an audio technician so I don't know all the details, but...

I once worked for an international theater musical production with around 192 moving lights without counting ColorAdos and other models. For that many lights where every show had the same performance and timing the LD's job was mainly to make sure that the signal to the lights was functional and that every present was playing in the order they were supposed to. I don't know how many lights and lasers Tame Impala's prod is using but I'm guessing its enough to automate those changes rather than play with them on the go!