In order to take advantage of the Delay Until Date on Contact element within SimplyCast 360 you'll require a date and time stored in your list with the following format:
YYYY-MM-DD HH:MM:SS
2015-06-28 13:30:00
Note that the HH:MM:SS is not required, if it's neglected will assume 00:00:00 which is midnight for the date specified.