Not all App Templates allow for editing time on a date field. On the Edit app template if a new object is added or attributes edited the ability to edit the time is available as it is on the web map, however on the Find Edit Filter app it is not available nor is it possible to access the time portion of the date field on the out of the box Web AppBuilder edit widget.
Currently, the ability to enter time data in the "Out of the Box" Edit widget is not available. If you have the WAB Developer Edition, you can download the app and edit the widget's code to show the time field.
Esri is planning on fixing this for the UC Release.
Here is the thread that has the fix for Developer Edition and where Esri confirms that this will be fixed.
Hope that this helps!