Simplistically variable pitch props do whatever they have to do to maintain the engine RPM that you set on the lever in the cockpit.
The props will always be at max fine pitch when they can't reach the RPM that you have requested.
That's why I do a double take on looking at the props of museum aircraft. The props should always be on the fine pitch stops unless feathered.
And that's why you exercise the CSU before take off. If you don't you will have cold oil in the prop control system giving you sluggish prop control as you feed in the power.