I don't think time, itself, is movement, in the same way that a direction is not movement. You can move _in a direction_ but the direction isn't the movement, Same thing with time. Time is a direction. One can move through time, but it's not the _time_ that is moving. In our reality, everything is moving through time, so when that magnetic field "changes with respect to time" it is changing in space-time, and because time is a constant, it drops out of the equation, and all you can talk about is it's movement through space.
Also, when you say the magnetic field is moving, what is causing this movement? And the other question in this scenario is, what is _generation_?
Lets begin with generation. Power generation is basically a conversion of energy from some non-electrical from to electrical (where it can be used to power electronics devices).
A moving magnetic field could be caused by an stationary electromagnet with a transitioning current, but it takes electrical energy to generate that current, so all you would have is a transfer of electric power, not a generation of it.
It could come from a permanent magnet, but if the magnet is constrained by the rule of _no motion_, then the field of the magnet would have to be modulated somehow. One way might be to heat the magnet beyond it's curie point, thus causing the magnetic field to collapse which would induce a voltage in a nearby wire(s). But, that doesn't sound very efficient. Might be useful as a sensor, though