Well, door frame need not be supported just at the base, it can also be supported on its vertical side, so need not have to 'root' it in the base cement. If you do door frame first, just ask how do you cut the tile nicely to fit the edges against the frames edges which are not straight? The tiler will simply use grouting which is unsightly to fill the gaps. Just take a look at my frame sitting on tile, perfect edges. My advise, do tile first, then frame.