I have a question if this requires customizing or if I have missed a means of having this work out of the box.
Web Map. Configuring Popup, you can select to have Time included with Date field (Configuration)
As seen here:
The change would produce the following in a feature popup:
In the Web application Query widget... pointing to the same layer... If a Query is Initiated, the result as well as the Popup when clicking on the result shows the following: (No Time)