A time stamp field can only be queried by exact match, so a date picker field cannot be used to query it.
a timestamp stores the data in the format:
when querying the time stamp, you need to match the entire time stamp including the time portion.
a datepicker will only send the year month day portion of the date. since it doesn't include the time portion, it will not be able to make a match.
as for dis[p;laying it on the results page, it probably uses the date function and converts the format to not include the time, you could edit the formatting to include the time,