It's worth checking on the Stanford Encyclopedia of Philosophy when this kind of issue comes up. It looks like this view - emergent=hard to predict from low-level model - is pretty mainstream.

The first paragraph of the article on emergence says that it's a controversial term with various related uses, generally meaning that some phenomenon arises from lower-level processes but is somehow not reducible to them. At the start of section 2 ("Epistemological Emergence"), the article says that the most popular approach is to "characterize the concept of emergence strictly in terms of limits on human knowledge of complex systems." It then gives a few different variations on this type of view, like that the higher-level behavior could not be predicted "practically speaking; or for any finite knower; or for even an ideal knower."

There's more there, some of which seems sensible and some of which I don't understand.