The rediscovery of the Earth under the New Empire, near the end of the book, is dated to 560 million years hence. The later Asteromorph shown here is of the kind that defeats the Gravitals and founds the New Empire itself. The empire is said to last "millions of years", but presumably not hundreds of millions; it stands to reason that the later Asteromorphs here would have evolved around 500 million years hence, and not much earlier.
People, the latter Asteromorphs are supposed to live up to 500 million years in the future. 500 million years ago, our ancestors looked like this (see step 11 here). If you looked at a jawless proto-fish in the Cambrian, would you imagine its flank muscles turning into human hands or bird wings? The changes in Asteromorphs aren't that extreme.
What an impressive illustration! Wonderful job.