I see this problem as well. I think I know what the problem is. In every case it happens to me, there has been a break in the recording from one scene to another. In the original VHS video, that break from one scene to another is also one where the recording is slightly garbled as it is transitioning. The software seems to try to "help" by inserting a short green screen break between the scenes. Every point at which the Roxio software inserts this green screen, the audio gets a tiny bit more delayed because it also introduces an audio silence that is a bit longer than the green screen.
If a video doesn't have many of these, the "easy" way of avoiding the problem is to stop recording, then start again with a new recording beginning with the next scene. Since I typically introduce transitions, titles, etc between scenes, this does work. Still, it's a giant pain in the butt that this problem has existed so long.
I was hoping there would be a way to stop the software from "helping out" by inserting the green screens, but I don't see a way to do that.