Fred, I am referring only to a beveled Turpin style tip, not a wing bone. I use it with the opening ( flat part of the bevel)to my left side. That way both lips contact the opening as explained in Turpin's book. I found this worked much easier and added more realisim to my calling than having the bevel up or down. Just another idea for folks to try. Not mine but Turpin's, if you interpret what he writes literally.
A beveled tip is directional. You just can't throw it up and start calling in any position as with a rounded tip that is cut off flat. That said, I like a mouthpiece tip that is cut off flat with a slightly rounded edge. The degree of angle from the main part of the mouthpiece to the tip and the final OD of the tip make a difference in how easy the call plays and sounds too.
Check out how other guys play their calls and adopt the one that works best for you. No method is set in stone.
Ralph