Hi Frank,
This phenomenon is called FOUC, and is not caused by the search plugin. It happens, when the site stylesheet files are loaded asynchronously instead of during the regular page load – and the yet unstyled items flash until the CSS file is loaded.
Usually Cache plugins have this feature, but is disabled by default Try checking your cache plugin options for asynchronous CSS loader feature or something similar.
Some CDN providers may also offer a Stylesheet Lazy Loader, Rocket Loader or similar features – which will result in this issue. These should be used very cautiously, and critical CSS must be validated and generated first, which is not an easy task.