Do when you go to : search/test where you want to search the database for "test" and you have deafult index that is called main_index then you see the message that there is no default index selected. The cause of this cause in the function : _sphinx_search_page you have the code :
if ($path) {
$iid = _sphinx_get_index_by_path($path);
}
else {
$iid = _sphinx_get_index_by_name(variable_get('sphinx_default_index', null));
}
the idea is the you need to remove the else here. Cause right now it tries to load the "test" index and bacause it doesnt find it it return an error that the deafult index is not defined. The code should look like this :
if ($path) {
$iid = _sphinx_get_index_by_path($path);
}
$redirect = false;
if(!$iid){
$iid = _sphinx_get_index_by_name(variable_get('sphinx_default_index', null));
$redirect = true;
}

Also after you load the index object it is nice to redirect to the correct url corresponding of the index you are searching in :
if($redirect){
drupal_goto('search/'. $index->index_name. ($path ? '/'. $path : '' ) );
}
This way you are sure that you are always on the correct page that corresponds to the index you want to search in.
This allows adding blocks with exended search forms :)