I am replacing our tub with a tiled shower. I am moving the drain to the center. Does the new drain for the tiled floor mount flush with the existing subfloor. The drain I purchase is labelled for tiled shower and has a bevel edge on the widest part of the drain and a screw drain to accommodate the pan mud.

" Does the new drain for the tiled floor mount flush with the existing subfloor?"

You will install a flange type shower drain,(see image) ON the subfloor. No need to recess it. Run your pan up the wall 8 inches and make your corners seamless.
Good luck, Tom