Typically when I set an exterior door that is on a slab, I mix up a bit of modified thinset, the type used for setting tile in showers. I will set the door in place, as you may have already done, shim the threshold level, mark the shims so if they get disturbed they can be set back in place. Place thin set all over the area the threshold was, governing how much you set in place based on the gaps you notice after the door was dry fit in place. Before you add the thinset, you will need to remove the cement you put in place. Be certain the floor is clean so the thinset gets a good seal to the floor. Set the door back in place, settling the door into the thinset. Shim the door in place with shims at all 4 top and bottom corners. At the corners, not near the corners and drive them in snug and set a screw or even a nail at both top corners. Driving shims any other place along the jamb will bow the jamb badly at this time.
Scrape and clean all excess thinset from the sill and repack any missing areas if needed. Be certain the door has settled down all the way and be certain the gap is proper at all the corners. You will have removed the shims UNDER the sill by the time you start the first cleanup. The shims at the corners are to remain. After the first cleaning, you will be able to tell if the door is settling more by the way the thinset bulges out since it has been cleaned. Do not use water yet for cleaning you will make a mess of the thinset shim if done too early. You have about an hour working time to get everything nice and clean. The exception is if the thinset gets on top of an aluminum threshold. It grabs onto that rather quickly so you may want to clean that up before a half hour passes, or just don't get any on it.... With all the major leveling and squaring and leveling done, finish shimming the door and fastening it in at the hinges, latch and midway both above and below the latch, minding the gap all around the door, keeping it even. With the door set 100% now return to cleaning the thinset the rest of the way. If there is any more to scrape or even dry brushing with a stiff bristle brush, do so, the less you have to clean with a sponge and water the better. You need to do all you can to keep from re-wetting the thinset or it will sag out if it is too thick. With a well rung out sponge, wipe up the left over thinset The thinset should never look shiny, if it does, there is too much water in the sponge. Squeeze it out really hard and keep wiping till all excess thinset is gone and leave it to cure for 2 days before opening the door. Lock it, hide the key. If the threshold is stepped on too soon, it will squeeze out the support the thinset could have made. If it receives its initial strength after one day and stepped on, it will separate from the threshold and will start to fail. Leave it be, and it will last as long as the door will or the building.