Fist go to Systems-User Profile-Own data-Defaults(TCode: SU3) and change the date format to DD.MM.YYYY, save and logg out from system.
Log in again and now you start doing the LSMW recording once again. The recoding which you have mentioned is absolutely correct,but the start date you have given is 01.01.1900(this you need to check from when you are going to create the position or relationship and give the actual date) and save.
Now when it comes to field mapping, you have do decide whether you want to map the date using source field you have defined in third step of LSMW or you want to give a default date.
If its a default date then go to Constant which is there in the heading top right and give the start date as 01011900 and end date as 31129999 and save
Now you try reading the data, i hope it will work, if not please let me know.