New constuction

Should doors and jambs be installed before or after laying backerboard and tile?

You can install them after the tile is in, just install any saddles that go in after the door is hung. Are they prehung doors?

I'd install pre hung doors before, sometimes the jambs are not the same length and with getting the door set right, odds are both jambs won't sit flush on the tile. Install them first and use a jamb saw to undercut them.

BTW - we set the hinge side of the doors on a quarter inch block, that way you have some wiggle room and it seems to always be high enough to clear carpet and not to high for laminate/tile.