As of now, the board drop-down in the sidebar lists all boards associated with the project alphabetically, and the first time you access a project with project centric navigation enabled you'll see the first board in this list. If you change the board and navigate away from the project centric view, the next time you return to the project, you'll see the last board you were viewing. I know this may not be the best in some scenarios and as of now, a 'default' board cannot be automated to show in the new project navigation upon selecting a specific project.

Instead of this behavior, the ability to select a specific Kanban or Scrum board to display every time upon selecting a project when having multiple boards associated with a project would be beneficial to some users.