I have been using WP-TwitterSearch, by James Fleeting, for some time. However, regardless of where, in my wordpress blog post, I place the shortcode the content(the twitter search results) always displays at the top of the post.
Another user of this plugin asked about this issue 7 months ago http://wordpress.org/support/topic/304942. I sent an email to the author of the plugin regarding this issue about 1 month ago, but the author did not respond.
So, apparently, the author of this plugin, for whatever reason(s), is unable to resolve this issue. It is a free plugin, though, and, I do understand that the author is, presumptively, under no obligation. I have made this post in the hopes that someone can tell me how to resolve this issue.
Incidentally, I also use the WP List Tweets plugin, by Marty Thornley, http://wordpress.org/extend/plugins/wp-list-tweets/changelog/ and, apparently, he resolved an issue similar to the issue I am facing with WP-TwitterSearch.