The DB determines relevance, not Connections, so Connections displays the order based on relevance that the database determines. Connections can only do the relevance sorting if the database itself supports it.
Some things you can help narrow the search results, navigate to the Connections Settings admin page and click the Search tab. Enable search for only the minimum fields you need to be searched. The more fields, the more possible returned results which may or may not make sense in your context.
You can also try disabling the “Keyword Search” search option leaving only the “FULLTEXT” option enabled. The FULLTEXT search is, if your database supports it, is what will return relevance based results. If you disable the keyword search option and you get no results when performing searches, then your database does not support it and you will have to rely on the keyword search.
Hope this helps!