When I reach our local frost depth of 48 inches, I add about 6 inches of stone to the bottom of the hole.
This provides a good base for the footing, which consists of 6 inches of concrete to tie all the rock together and an additional 6 inches for anchoring the tube form.
I press the bottom of the tube a couple of inches into the wet concrete, careful to keep it plumb, level, and at the proper elevation at the top.
I add dirt and rocks around the tube, tamping as I fill to prevent voids, until I'm about halfway up.
As I fill the tube, I add in clean rock, careful to keep it in the middle of the pier so there are no voids on the outside surface.
Before I place the last 6 inches of concrete, I install three lengths of #4 rebar. I drive them all the way to the bottom of the footing, which should prevent the footing and pier from ever separating.
After placing the last of the concrete, I let it set for a few minutes, then tap the top surface with a straightedge to help push down any aggregate.