That said, knowing that the choice is predetermined and knowing the choice, is often very different.
For simple systems if you know the initial state you can easily predict all the future states by using a formula and not doing the computation the system performs.
But for many systems like rule 30, the only way to predict the future state is to perform exactly the computation the system is performing. So if the TM describes a person, the only way to know future states of the TM from initial state is to wait for the person in the TM to make the choice.
In Conways example, free will would be if experimenters decision what to measure is based on the state of the part of the universe describing the experimenter alone, and not connected to the parts describing other experimenters performing related measurement.