For example, the spacetime explanation for gravity is also a model, and is also likely to be an "illusion." Making note of that is theoretical physics 101... or at least it should be.
You say that like it's so obvious. But why do they move in the first place?
The answers seems to be "physics doesn't have to abide by your intuition or need for narratives, human"
Outside of that there really isn't a 'reason'. This isn't how physics works, although it's certainly in our nature to create and expect meaning and cause everywhere. Brain is bound to think in hierarchies, because that's how it's built to operate, but the universe doesn't have that limitation.
And what's the difference between this and saying they experience a force?