Hi,
In general, anything that is purely made of user-defined terms shouldn't update with time automatically. J is the main place to put it, but you can also have time dependent material parameters (in particular, you can hide it in say, the FixedLayer). If you need something more flexible, I would recommend looking to a new feature in mumax3.11, that allows loading a custom time-dependent field from a file:
https://groups.google.com/g/mumax2/c/pR3jEAdShBo/m/6tBg1oxDAAAJIs there something specific you're trying to achieve?
Best,
Josh L.