When reading a phylogenetic tree, is it correct to assume that all ancestors (as represented by nodes) are distinct groups of organisms that are not represented in extant populations (at the tips of the branches)?

Another way of phrasing this question is, can an ancestor (as represented by the nodes on the tree) also be represented at the tip of a branch? Or are all common ancestors no longer in existence?

My initial inclination is to say that ancestors can only be represented by nodes and cannot be also considered extant species. But then I became confused when I was looking at the attached image showing speciation of butterflies. The image shows one group of butterflies representing both the common ancestor of the other species as well as its own extant species.

It depends on what the tree is depicting a bit.  Nodes by definition represent the ancestors of taxa at the tips, so represent an earlier point in the evolution of the lineage.

However, remembering that species designations are a bit arbitrary anyway (search this site for questions on species concept for more), just because a lineage "splits" it isn't necessarily the case that both descendent lineages have accumulated sufficient change from their shared ancestor to be designated as new species.