If I get the notion of 'primitive' the SEP has in mind. This makes sense to me.
There are measures that can only be taken of the composite, and there are effects that can only be observed upon those measures by other measures that can only be taken at a similarly high level. So these are causal relations between things that cannot be stated in terms of the lower level attributes.
For instance, it seems clear that the decisions of corporations supervene from the psychological and physical needs of their individual employees, customers and stakeholders. But there are also causal forces that act upon corporations only as whole entities. For instance, we can see that monopoly has certain advantages, and a corporation may work hard to enter a market where it can secure and leverage a monopoly, perhaps by collecting patents.
But what is a monopoly in terms of individuals' needs? Monopoly, and more generally the concept of market-share, is a new driver of corporate action that arises only at the level of the whole corporation and relates mainly to other corporation-level and market-level drivers. Although they clearly proceed in detail from lower-level psychological or physical needs, its effects cannot be analyzed in terms of those alone. It is in that sense 'primitive' at this level.
Similarly, the notion of heat flowing through a space, or of osmotic pressure driving diffusion or of a certain pH causing corrosion can only be observed at a macroscopic level. We can prove how these effects are actually determined by statistical trends in molecular behaviors, so they supervene upon that lower-level behavior. But we cannot measure them or actually see their effects from that level. They are 'primitively chemical' as opposed to 'molecular' forces, and in that sense grossly chemical behavior is emergent from molecular behavior.
Likewise, mind may be emergent at the level of decision-making although it supervenes upon biological activity. We may observe mental processes that proceed from brain activity, but decisions may exhibit patterns that are not clearly discernable or describable at any lower level of organization.