index.php is the default template, the fallback.
If we look here:
http://codex.wordpress.org/Template_Hierarchy
And at the diagram:
We can see here that search.php is the appropriate template.
Have you considered using author.php and the author archives instead of modifying the search template? There are far better ways of implementing what you want, even the searching via author name, rather than acquiring a fix for your fix. Perhaps a new question titled “How to search posts via author name”