Can you check whether you are using an in-memory version of H2?
If so, I'm not sure whether you can see the tables from the web console of H2.
Well, the Demo Human Task Server does use the in-memory H2, however it hadn't occurred to me that this would make a difference in using the H2 console.
However, on Friday (after posting) I did have some suspicion, because when working with the GWT Console I was in fact able to see the data in the H2 console.
So I'll have to mark this one answered.
P.S. I suppose the H2 engine and the H2 console servlet must run in different JVMs. That would explain it.