Illusion is just the word they try to use to explain what emergence is. I don't think illusion really fits all that well though because illusion implies it's somehow not real and that's not what emergence is about.

Emergent things are real (in the sense of Dan Dennett's real patterns) just not fundamental.

I agree. As a metaphysical ponderer, I often consider how "illusion" is fundamental to our understanding of science. Consider this: all physical laws and theories are verified through human experience on a time scale, ie: under these conditions, you will observe this result. There is always an observer and at least two points in time. Time, and observation of it, is the ground truth of all physical laws, of our very experience of the universe.

A notion is an illusion when it appears to be experientially necessary but models without its structure consistently outperform models with said structure at predicting outcomes.

To you personally in everyday life, or in general?

Because they're concerned with the latter.