Views Search is displaying no results behavior by default
I assume you are using the "On empty input: Show none" option of the search terms filter.
In this case the view is actually still running but returning no results due to the filter, so you get the empty text displaying.

To stop that you can change the "Exposed form style" to "Input required".

Then the view will not run until a search term is entered, which means no unwanted empty text.