Why boot picker doesn't work?
If you press Option key (on Mac keyboard) or ALT (on Windows keyboard) and there is no reaction on boot, but instead computer is booting OS, then you might be using some non-standard USB 3.0 card.
Make sure to connect your keyboard and mouse to the built-in rear USB 2.0 hub inside Mac Pro. This should resolve the problem.
If you still cannot see boot picker you might need to use underscan feature in your display's OSD.