When installing floor tile in a finished room, it's better to slide the tile under door casings rather than fit it around them. You'll end up with a better-looking floor. If you butt the tiles against the casings (Photo 1), you'll usually end up with uneven gaps that you have to fill with grout. The gaps won't look good, and chances are the grout will crack from the vibration caused by the closing door.
Cutting the casings is fairly easy and only takes a few minutes if you have a sharp handsaw or special “jamb” saw. Simply place a tile next to each casing, add 1/8 in. for the adhesive thickness (use 1/8-in.-thick cardboard as a guide), mark the casings and saw at the mark. Sliding the tiles under the casings eliminates the need for grout and hides the cut edges (Photo 2).