Ernest
The Live Search Trigger is set to 4 characters, but the system behaves as if set at 0. I have cleared the cache. Even when the option is turned off, it still behaves as a 0 is set, that is on loading a page with the Search Pro widget set it starts returning the previous search results. The same happens if the WP search widget is used.
The dedicated search page behaves in a similar way.
You have the auto-populate feature enabled. That automatically starts the search event regardless of the number of characters set. Make sure to turn it off and the results will not display initially until 4 characters are entered.