When adding a task, can set the “Start date and Start time, Due date and Due time”.
Similarly, in the template, I would like to set the “Start date and Start time, Due date and Due time”.
Currently, it is set as “Start date, Due date and Due time”.
Would like to bump this post, as I have stumbled into the same problem.
It still does not seem possible to assign a “Start time” when working with task templates. This would be highly beneficial for boards using the Day view in the Timeline view, where tasks require start and end time to show up 
Hope this could be fixed!
