I ran into this interesting state in project server last week and was able to resolve it this morning. You may find that the timer job never executes itself..why? Have no clue! Especially since we already ran it three times previously and it always worked!
So I figured a way to successfully fire it manually from PowerShell:
$job = get-sptimerjob -id 4d9b0bd6-2919-4256-b030-c9d50c168e57
$wa = get-spwebapplication https://projects.contoso.com
Keep in mind that rather execute in the owstimer process it will run as the current PowerShell user. That user must have access to the database server to apply security and create databases.