This post is an explanation of how Scheduled Smart Lists work with start dates.
Normally for any Smart Lists, all tasks are shown on List view.
On Day, Week and Month views, you'll see tasks that are due on that selected time frame. If you have 'Use Start Date' option turned on, tasks that have start date passed but not due will be shown too.
Scheduled Smart Lists work similar to this. For example, let's assume it's 'Today' filtered scheduled smart list. On List view, tasks that due today are shown.
If you have 'Use Start Date' option turned on, it'll also show tasks that start date has passed but due date has not. But there is an option on 'Edit List : Filter' named 'Due Date' where if you turn it on, tasks that are only due on that date will be shown.
You can see details by example on below image (Sorry about bad writing )