I have installed a fresh Magento 184.108.40.206 store (not from upgrade). I have set Search Type=FullText in Catalog Search configuration. I also have set Use in Quick Search=Yes only for the attribute name. However when I search for a product using Quick Search, I get every product listing whose title (i.e. name) contains any of the words I put in the text field of Quick Search.
I also reindexed data and refreshed the cache from the administration GUI. I also cleared cache manually by removing the files under /var/cache but the problem persists.
I use the default themes that come with Magento package. The problem occurs with any theme. In my opinion, the Quick Search seams to return any product listing that contains any of the words in its title (name attribute) specified in the search string.