Shouldn't "starts" be referring to its inner edge and not its outer edge? When talking about the present day Kuiper Belt, we would say it starts just beyond the orbit of Neptune and ends at 50 AU, rather than saying it "starts" at 50 AU and ends at the orbit of Neptune.

But, you're right, he could mean it the way you say since there's probably no definitive way to use the words "starts" and "ends" when referring to orbiting disks.

However, I still think he means it extends away from Neptune, not towards the Sun. The 4 gas giants would have swept the area interior to Neptune clear during their formation, but further than Neptune, where orbital velocities ,and hence accretion, are slower, there is still abundent mass is still in the form of planetesimals.

In figure 1, there's virtually no migrating going on in the 1st 100,000 years. I'd expect migration during this period if the planets were embedded in the disk during this period. This period of almost no migration lasts until a very small migragion by Saturn places it in the 2:1 resonance and kicks Uranus and Neptune outward into the disk of planetesimals. Then once inside this disk, they scatter the disk and their migration accelerates as a result. They kick some objects in towards Jupiter and Saturn, which causes them, especially Saturn, to migrate as well. Just my guess...